Planck Star Remnants in LQG

• Planck Star Remnants are quasi-stable endpoints of gravitational collapse in Loop Quantum Gravity, where quantum bounce replaces classical singularities at Planck density.
• They form through modified Friedmann dynamics and quantum tunneling that drives a black-hole-to-white-hole transition, yielding remnants with near-Planckian horizon areas and extensive interiors.
• PSR are considered potential dark matter candidates, emerging as relics from evaporated primordial black holes with signatures that depend on quantum gravitational corrections and effective geometries.

Searching arXiv for recent and foundational papers on Planck star remnants and related scenarios. arXiv search query: Planck star remnants dark matter loop quantum gravity white hole remnants Planck Star Remnants (PSR) are quasi-stable, Planck-scale end states of gravitational collapse that arise in quantum-gravity scenarios where the classical singularity inside a black hole is replaced by a bounce at critical density. In the reviewed Loop Quantum Gravity (LQG) and Loop Quantum Cosmology (LQC) framework, a collapsing matter distribution reaches an ultra-dense Planck star phase, the exterior geometry undergoes a black-hole-to-white-hole transition through quantum tunnelling, and the late-time object is a remnant with near-Planckian horizon area and a large interior (Rovelli et al., 2024). Across the recent literature, PSR are treated either as white-hole-like remnants stabilized by LQG discreteness (Rovelli et al., 2024), as stable non-radiating Planck-mass relics formed after Hawking evaporation (Trivedi et al., 3 Jun 2025), or as static horizonless Planck-scale compact objects supported by effective loop-quantum corrections (Wilson-Ewing, 2024). Their significance lies in the conjunction of singularity resolution, black-hole information retention and release, and the possibility that such relics form a component of dark matter (Rovelli et al., 2024).

1. Conceptual definition and physical picture

In the LQC-inspired collapse scenario, a Planck star is the ultra-dense state reached when quantum-gravity repulsion halts collapse at a critical density and triggers a bounce (Rovelli et al., 2024). The effective Friedmann equation is modified to

$$\frac{\dot{a}^2}{a^2}=\frac{8 \pi}{3}\,\rho\left(1-\frac{\rho}{\rho_c}\right),$$

with critical density

$$\rho_c=\frac{\sqrt{3}\,c^2}{32\pi^2\,\gamma^3\,\hbar G^2}\sim \frac{c^2}{\hbar G^2},$$

so that the scale factor reaches a minimum and re-expands (Rovelli et al., 2024). In a related phenomenological description, Planck stars form when the collapsing shell reaches the Planck density

$\rho_\mathrm{P} = \frac{c^5}{\hbar G^2},$

and rebounds outwards (Tarrant et al., 2019).

A Planck Star Remnant is the quasi-stable object left at the end of the black-hole-to-white-hole transition, with a horizon of near-Planckian area and a large interior (Rovelli et al., 2024). In the reviewed LQG account, the remnant is best understood not as a purely classical white hole, but as a quantum superposition of black- and white-hole horizon states, stabilized by the minimal nonzero area eigenvalue of the LQG area operator (Rovelli et al., 2024). The same literature also treats PSR more generically as Planck-mass relics, i.e. stable endpoints at approximately the Planck mass after Hawking evaporation stalls (Trivedi et al., 24 Sep 2025).

The broader conceptual picture differs across constructions. In the black-to-white transition scenario, the remnant retains a large interior volume and a memory of the progenitor through that interior geometry, while its horizon mass is near the Planck scale (Rovelli et al., 2024). In the Trivedi–Loeb model, the bounce remains causally hidden and no observable white-hole outflow is assumed; the end state is instead a stable, non-radiating Planck-scale core with radius asymptoting to the Schwarzschild radius as the black hole mass approaches the Planck mass (Trivedi et al., 3 Jun 2025). In the effective static construction, the endpoint is a horizonless miniature star with Planckian mass and radius, obtained from an effective Tolman–Oppenheimer–Volkoff equation rather than from a tunnelling transition (Wilson-Ewing, 2024).

2. Formation mechanism and effective geometry

The reviewed black-hole evolution scenario has three linked ingredients: an interior bounce, an exterior tunnelling transition, and a global spacetime construction that remains classical outside a compact quantum region (Rovelli et al., 2024).

For the interior, the collapsing star follows LQC effective dynamics. The boundary radius obeys

$\dot r_b^2=\frac{2m}{r_b}-\frac{A\,m^2}{r_b^4},$

which exhibits a short-distance repulsive “quantum pressure” (Rovelli et al., 2024). This effective repulsion is the mechanism by which the singularity is replaced by a bounce.

For the exterior, the effective spherically symmetric metric is Schwarzschild-like with a quantum correction,

$$F(r)=1-\frac{2m}{r}+\frac{A\,m}{r^4},\qquad A=\frac{3}{2\pi\rho_c}\sim \hbar,$$

with outer and inner horizons

$$r_+\simeq 2m,\qquad r_-\simeq\left(\frac{A\,m}{2}\right)^{1/3}.$$

The geometry outside the star tunnels from a trapped to an anti-trapped configuration, so the transition is formulated as a black-hole-to-white-hole tunnelling process (Rovelli et al., 2024).

The global exterior can be built as a single-asymptotic-region cut-and-paste spacetime that is compatible with exact general relativity outside the compact quantum region, denoted the $B$ region. In this construction, the transition is consistent with the local Birkhoff theorem because the nonclassical dynamics are confined to the compact high-curvature domain (Rovelli et al., 2024). This point is central to the claim that the scenario avoids singularities without requiring modifications of low-curvature exterior GR.

A distinct but related approach is given by Trivedi and Loeb, who analytically match a homogeneous FLRW interior to an exterior Schwarzschild spacetime using the Israel junction conditions (Trivedi et al., 3 Jun 2025). Their interior metric obeys

$$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho \left(1 - \frac{\rho}{\rho_c}\right),$$

with bounce at $\rho=\rho_c$, and the matching condition at the boundary is

$R(t) = r_0 a(t).$

The paper emphasizes that the bounce and re-expansion occur within the event horizon, so external observers are causally disconnected from the re-expansion (Trivedi et al., 3 Jun 2025). This suggests a remnant scenario in which the internal nonsingular dynamics need not yield an externally visible white-hole phase.

A third line of work derives effective LQG dynamics for spherically symmetric spacetimes with perfect-fluid matter and finds static Planck-scale objects from the quantum branch of the effective equations (Wilson-Ewing, 2024). In that framework, the improved-dynamics polymerization scheme uses $$\rho_c=\frac{\sqrt{3}\,c^2}{32\pi^2\,\gamma^3\,\hbar G^2}\sim \frac{c^2}{\hbar G^2},$$0, the homogeneous limit reproduces the LQC effective Friedmann equation

$$\rho_c=\frac{\sqrt{3}\,c^2}{32\pi^2\,\gamma^3\,\hbar G^2}\sim \frac{c^2}{\hbar G^2},$$1

and the static sector yields an effective TOV equation whose quantum branch supports horizonless compact solutions (Wilson-Ewing, 2024).

3. Mass scale, area gap, and lifetimes

In the black-to-white transition framework, the remnant mass is fixed by the LQG area gap. The minimal nonzero horizon area is

$$\rho_c=\frac{\sqrt{3}\,c^2}{32\pi^2\,\gamma^3\,\hbar G^2}\sim \frac{c^2}{\hbar G^2},$$2

which leads to a Planck-scale remnant mass

$$\rho_c=\frac{\sqrt{3}\,c^2}{32\pi^2\,\gamma^3\,\hbar G^2}\sim \frac{c^2}{\hbar G^2},$$3

Heavier remnants are not expected because of the area gap, while lighter-than-$$\rho_c=\frac{\sqrt{3}\,c^2}{32\pi^2\,\gamma^3\,\hbar G^2}\sim \frac{c^2}{\hbar G^2},$$4 remnants are forbidden by area quantization (Rovelli et al., 2024).

This specific mass-fixing mechanism distinguishes PSR from generic Planck relic proposals. In the 2025 cosmological abundance analysis, the relic is treated sharply at the Planck mass $$\rho_c=\frac{\sqrt{3}\,c^2}{32\pi^2\,\gamma^3\,\hbar G^2}\sim \frac{c^2}{\hbar G^2},$$5, and one relic is assumed to form per evaporated primordial black hole (PBH) (Trivedi et al., 24 Sep 2025). The Trivedi–Loeb analysis likewise assumes $$\rho_c=\frac{\sqrt{3}\,c^2}{32\pi^2\,\gamma^3\,\hbar G^2}\sim \frac{c^2}{\hbar G^2},$$6 and infers the number density required for dark matter from that mass scale (Trivedi et al., 3 Jun 2025).

The timescale structure is multi-layered. The Hawking evaporation time scales as $$\rho_c=\frac{\sqrt{3}\,c^2}{32\pi^2\,\gamma^3\,\hbar G^2}\sim \frac{c^2}{\hbar G^2},$$7 in Planck units, with SI expression

$$\rho_c=\frac{\sqrt{3}\,c^2}{32\pi^2\,\gamma^3\,\hbar G^2}\sim \frac{c^2}{\hbar G^2},$$8

The black-to-white transition probability is nonperturbative and exponentially suppressed for $$\rho_c=\frac{\sqrt{3}\,c^2}{32\pi^2\,\gamma^3\,\hbar G^2}\sim \frac{c^2}{\hbar G^2},$$9,

$\rho_\mathrm{P} = \frac{c^5}{\hbar G^2},$0

so tunnelling becomes likely only once evaporation has reduced the black-hole mass to the Planck scale (Rovelli et al., 2024).

The duration of the transition itself, as seen by asymptotic observers, scales with the current mass as

$\rho_\mathrm{P} = \frac{c^5}{\hbar G^2},$1

with an additional redshift-driven factor $\rho_\mathrm{P} = \frac{c^5}{\hbar G^2},$2 in the exterior construction (Rovelli et al., 2024). In the older phenomenological tunnelling literature, a different scaling

$\rho_\mathrm{P} = \frac{c^5}{\hbar G^2},$3

was widely used to estimate present-epoch explosions of subsolar PBHs, implying observable events today for masses $\rho_\mathrm{P} = \frac{c^5}{\hbar G^2},$4 (Tarrant et al., 2019). The 2024 review explicitly distinguishes the near-Planckian remnant scenario from such earlier-tunnelling proposals and states that ultra-soft remnant emission, rather than energetic transient outbursts, characterizes the long-lived PSR picture developed there (Rovelli et al., 2024).

The remnant lifetime after formation is argued to be long because the object must re-emit the information content associated with the earlier Hawking radiation using only $\rho_\mathrm{P} = \frac{c^5}{\hbar G^2},$5 energy. The resulting lower bound is

$\rho_\mathrm{P} = \frac{c^5}{\hbar G^2},$6

derived from information-theoretic considerations (Rovelli et al., 2024). In the specific emission model,

$\rho_\mathrm{P} = \frac{c^5}{\hbar G^2},$7

with very low characteristic emission energies (Rovelli et al., 2024). This long lifetime is a necessary ingredient in the dark-matter interpretation, since relics must survive at least to the present epoch.

4. Quantum state, stability, and information recovery

The microphysical stability claim rests on LQG discreteness and on the conjugate relation between horizon area and radial extrinsic curvature. In the reviewed scenario, the remnant settles in the minimal nonzero area eigenstate, and because the area $\rho_\mathrm{P} = \frac{c^5}{\hbar G^2},$8 and radial extrinsic curvature $\rho_\mathrm{P} = \frac{c^5}{\hbar G^2},$9 are conjugate, an eigenstate of $\dot r_b^2=\frac{2m}{r_b}-\frac{A\,m^2}{r_b^4},$0 has maximal spread in $\dot r_b^2=\frac{2m}{r_b}-\frac{A\,m^2}{r_b^4},$1. The resulting state is written as

$\dot r_b^2=\frac{2m}{r_b}-\frac{A\,m^2}{r_b^4},$2

The remnant is therefore a quantum superposition of white-hole and black-hole horizon states rather than a classical horizon of either type (Rovelli et al., 2024).

This construction addresses the usual objection that macroscopic white holes are classically unstable to infalling perturbations. The review states that for Planck-scale horizons, triggering the classical instability would require trans-Planckian wavelengths, which quantum gravity likely forbids (Rovelli et al., 2024). A plausible implication is that the instability argument against classical white-hole remnants does not directly extend to Planckian quantum remnants.

The entropy and information argument is equally central. The Bekenstein–Hawking entropy is

$\dot r_b^2=\frac{2m}{r_b}-\frac{A\,m^2}{r_b^4},$3

The reviewed framework rejects the assumption that the number of internal states accessible inside the horizon is bounded by $\dot r_b^2=\frac{2m}{r_b}-\frac{A\,m^2}{r_b^4},$4. Instead, as the interior volume grows while the horizon area shrinks, the number of interior distinguishable states can continue to grow, so the “central dogma” $\dot r_b^2=\frac{2m}{r_b}-\frac{A\,m^2}{r_b^4},$5 fails in the semiclassical regime (Rovelli et al., 2024). Hawking radiation remains mixed because it is entangled with negative-energy modes falling inward, and the information is retained until the remnant phase, after which it is slowly released through many low-energy quanta (Rovelli et al., 2024).

The dominant decay channel is not a prompt disappearance into flat space but multi-quantum emission of low-frequency photons or other light quanta carrying the trapped information (Rovelli et al., 2024). In the one-dimensional photon gas model used there, the total entropy to be emitted is $\dot r_b^2=\frac{2m}{r_b}-\frac{A\,m^2}{r_b^4},$6, the temperature scales as $\dot r_b^2=\frac{2m}{r_b}-\frac{A\,m^2}{r_b^4},$7, the number of quanta as $\dot r_b^2=\frac{2m}{r_b}-\frac{A\,m^2}{r_b^4},$8, and the lifetime as $\dot r_b^2=\frac{2m}{r_b}-\frac{A\,m^2}{r_b^4},$9 (Rovelli et al., 2024). This yields a picture in which most of the black hole’s energy is radiated earlier in thermal Hawking quanta, while the information emerges much later in an ultra-soft channel.

The static effective-LQG Planck stars of (Wilson-Ewing, 2024) raise a different stability issue. That paper derives explicit horizonless solutions with constant interior density $$F(r)=1-\frac{2m}{r}+\frac{A\,m}{r^4},\qquad A=\frac{3}{2\pi\rho_c}\sim \hbar,$$0, maximum compactness $$F(r)=1-\frac{2m}{r}+\frac{A\,m}{r^4},\qquad A=\frac{3}{2\pi\rho_c}\sim \hbar,$$1, and mass $$F(r)=1-\frac{2m}{r}+\frac{A\,m}{r^4},\qquad A=\frac{3}{2\pi\rho_c}\sim \hbar,$$2, but it does not perform a linear perturbation analysis or establish thermodynamic stability (Wilson-Ewing, 2024). This means that the existence of static solutions is not by itself a proof that such objects are dynamically realized or long-lived, although it does show that effective loop corrections can support Planck-scale compact objects without horizons.

5. Primordial-black-hole origin and dark-matter role

The principal dark-matter channel proposed in the PSR literature is formation from evaporating PBHs. In the 2024 review, remnants are presented as a dark-matter candidate requiring no new fields or modified GR, only GR plus quantum gravity (Rovelli et al., 2024). The preferred PBH progenitor mass window is obtained by requiring that Hawking evaporation complete before the present epoch while the remnant lifetime exceed the Hubble time:

$$F(r)=1-\frac{2m}{r}+\frac{A\,m}{r^4},\qquad A=\frac{3}{2\pi\rho_c}\sim \hbar,$$3

These correspond to Schwarzschild radii $$F(r)=1-\frac{2m}{r}+\frac{A\,m}{r^4},\qquad A=\frac{3}{2\pi\rho_c}\sim \hbar,$$4–$$F(r)=1-\frac{2m}{r}+\frac{A\,m}{r^4},\qquad A=\frac{3}{2\pi\rho_c}\sim \hbar,$$5, plausibly associated with reheating-era horizon scales (Rovelli et al., 2024).

For PSR of mass $$F(r)=1-\frac{2m}{r}+\frac{A\,m}{r^4},\qquad A=\frac{3}{2\pi\rho_c}\sim \hbar,$$6, the local number density is

$$F(r)=1-\frac{2m}{r}+\frac{A\,m}{r^4},\qquad A=\frac{3}{2\pi\rho_c}\sim \hbar,$$7

and using $$F(r)=1-\frac{2m}{r}+\frac{A\,m}{r^4},\qquad A=\frac{3}{2\pi\rho_c}\sim \hbar,$$8 the review states that this corresponds locally to roughly one PSR per $$F(r)=1-\frac{2m}{r}+\frac{A\,m}{r^4},\qquad A=\frac{3}{2\pi\rho_c}\sim \hbar,$$9, with a handful passing per $$r_+\simeq 2m,\qquad r_-\simeq\left(\frac{A\,m}{2}\right)^{1/3}.$$0 per year at galactic velocities (Rovelli et al., 2024). By contrast, the Trivedi–Loeb estimate takes $$r_+\simeq 2m,\qquad r_-\simeq\left(\frac{A\,m}{2}\right)^{1/3}.$$1 and $$r_+\simeq 2m,\qquad r_-\simeq\left(\frac{A\,m}{2}\right)^{1/3}.$$2, yielding

$$r_+\simeq 2m,\qquad r_-\simeq\left(\frac{A\,m}{2}\right)^{1/3}.$$3

and a total number in the observable universe of $$r_+\simeq 2m,\qquad r_-\simeq\left(\frac{A\,m}{2}\right)^{1/3}.$$4 (Trivedi et al., 3 Jun 2025). These quantitative differences reflect distinct remnant mass conventions rather than a disagreement about the basic relic mechanism.

The cosmological abundance problem was sharpened in 2025 by an analysis of PBH formation from primordial fluctuations (Trivedi et al., 24 Sep 2025). That work adopts the Planck-mass relic picture and computes the PBH collapse fraction $$r_+\simeq 2m,\qquad r_-\simeq\left(\frac{A\,m}{2}\right)^{1/3}.$$5 required for evaporated PBHs to leave enough relics to account for dark matter. Using the horizon mass relation

$$r_+\simeq 2m,\qquad r_-\simeq\left(\frac{A\,m}{2}\right)^{1/3}.$$6

the required fraction becomes less than $$r_+\simeq 2m,\qquad r_-\simeq\left(\frac{A\,m}{2}\right)^{1/3}.$$7 around $$r_+\simeq 2m,\qquad r_-\simeq\left(\frac{A\,m}{2}\right)^{1/3}.$$8 and reaches $$r_+\simeq 2m,\qquad r_-\simeq\left(\frac{A\,m}{2}\right)^{1/3}.$$9 near $B$0, corresponding to formation times $B$1–$B$2 (Trivedi et al., 24 Sep 2025). In that sense, viable PSR dark matter from PBHs requires very early-universe formation.

The same paper then argues that Gaussian initial conditions are incompatible with this dark-matter channel. For Gaussian perturbations with collapse threshold $B$3, the required PBH abundance implies a variance $B$4 and hence a curvature power-spectrum peak

$B$5

Such a large small-scale enhancement induces a stochastic gravitational-wave background in the LIGO band with peak amplitude $B$6–$B$7, above the LIGO O3 upper limit $B$8 (Trivedi et al., 24 Sep 2025). The conclusion is that Gaussian primordial fluctuations cannot produce enough PBHs to seed PSR dark matter without overproducing induced gravitational waves. The paper therefore leaves non-Gaussian primordial fluctuations as the viable channel for PSR dark matter (Trivedi et al., 24 Sep 2025).

This does not rule out PSR themselves; it rules out one specific cosmological formation pathway. The remnant hypothesis remains compatible with non-Gaussian PBH formation scenarios in which the required collapse fraction can be achieved with a smaller curvature variance and thus a weaker induced stochastic background (Trivedi et al., 24 Sep 2025).

6. Observational signatures, constraints, and competing phenomenologies

Observational expectations depend strongly on which PSR scenario is adopted. The long-lived remnant scenario reviewed in 2024 predicts direct-detection prospects through gravitational effects rather than high-energy explosive events (Rovelli et al., 2024). Quantum-sensing proposals using spatial superpositions of test masses or Josephson junction arrays could measure the phase shift caused by the gravitational field of passing PSR (Rovelli et al., 2024). Because the objects are cold, collisionless, and purely gravitationally interacting in that account, conventional electromagnetic searches are intrinsically weak.

The same review predicts diffuse ultra-soft remnant radiation rather than energetic bursts. The characteristic frequency is

$B$9

corresponding to $$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho \left(1 - \frac{\rho}{\rho_c}\right),$$0–$$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho \left(1 - \frac{\rho}{\rho_c}\right),$$1 for PBH progenitors in the preferred mass window (Rovelli et al., 2024). The radiation density grows linearly between the end of Hawking evaporation and the remnant lifetime, and then plateaus (Rovelli et al., 2024). High-energy transients are explicitly not expected in this end-of-evaporation remnant picture.

This contrasts sharply with earlier Planck-star phenomenology. Barrau and Rovelli proposed that black holes may hide Planck-density cores retaining memory of the initial mass, with a final explosion occurring at macroscopic scale rather than at the Planck mass (Barrau et al., 2014). In that model, the final mass is related to the initial mass by $$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho \left(1 - \frac{\rho}{\rho_c}\right),$$2 with preferred value $$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho \left(1 - \frac{\rho}{\rho_c}\right),$$3, and PBHs with $$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho \left(1 - \frac{\rho}{\rho_c}\right),$$4 and $$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho \left(1 - \frac{\rho}{\rho_c}\right),$$5 could reach the final stage today (Barrau et al., 2014). The characteristic size at explosion is $$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho \left(1 - \frac{\rho}{\rho_c}\right),$$6, which sets a primary emission scale $$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho \left(1 - \frac{\rho}{\rho_c}\right),$$7; after hadronization, the observable gamma-ray spectrum is expected in the tens-of-MeV range, with photon yield $$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho \left(1 - \frac{\rho}{\rho_c}\right),$$8 (Barrau et al., 2014). Under favorable PBH abundances, that paper estimated up to several short gamma-ray bursts per day with isotropic distribution from within a few hundred light years (Barrau et al., 2014).

However, low-frequency explosive Planck-star phenomenology is tightly constrained. The extragalactic background light analysis of (Tarrant et al., 2019) considers the $$H^2 = \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G}{3} \rho \left(1 - \frac{\rho}{\rho_c}\right),$$9 explosion scenario and finds that, for present-epoch explosions of mass $\rho=\rho_c$0, the total low-frequency energy per event must satisfy

$\rho=\rho_c$1

at $\rho=\rho_c$2 to avoid exceeding the observed isotropic radio–microwave–sub-mm background (Tarrant et al., 2019). The same paper derives constraints $\rho=\rho_c$3 or $\rho=\rho_c$4 for representative extended PBH mass functions (Tarrant et al., 2019). Since typical FRB radio energies are $\rho=\rho_c$5–$\rho=\rho_c$6, the required beaming or abundance suppression would be extreme, so PSR-origin fast radio bursts are strongly disfavored in that low-frequency explosive picture (Tarrant et al., 2019).

The literature therefore separates into two phenomenological branches. One is the earlier macroscopic-explosion branch, which motivated signatures such as FRBs, short GRBs, or MeV gamma bursts [(Barrau et al., 2014); (Tarrant et al., 2019)]. The other is the Planck-mass remnant branch, in which the late object emits very soft radiation on extremely long timescales and is more naturally probed either through diffuse low-frequency backgrounds or through direct gravitational sensing (Rovelli et al., 2024). Confusing these two branches is a common source of misunderstanding.

7. Relation to alternative remnant models and open issues

PSR are often compared with other black-hole remnant ideas, but the reviewed literature emphasizes several distinctive features. Relative to classical white-hole remnants, PSR are Planck-scale and quantum-stabilized through the LQG area gap and the superposition of horizon states (Rovelli et al., 2024). Relative to generic Planck-mass quasi-particles, they provide a concrete mass formula derived from area quantization rather than an ad hoc cutoff (Rovelli et al., 2024). Relative to GUP-induced remnants, the PSR scenario relies on the LQC bounce and LQG spinfoam transition amplitudes rather than modified uncertainty relations (Rovelli et al., 2024). Relative to stringy relic constructions, the review stresses that PSR require no new fields and keep semiclassical QFT and GR valid in low-curvature regions while rejecting the “central dogma” bound on interior states (Rovelli et al., 2024).

The static effective-LQG Planck stars of (Wilson-Ewing, 2024) represent a particularly instructive alternative. They are not white-hole remnants and not tunnelling products. Instead, they are static, horizonless, Planck-scale compact stars supported by holonomy-induced corrections in an effective TOV equation. For constant density $\rho=\rho_c$7, the pressure profile is

$\rho=\rho_c$8

with radius bound

$\rho=\rho_c$9

maximum mass

$R(t) = r_0 a(t).$0

and compactness

$R(t) = r_0 a(t).$1

These objects have Planckian mass and radius but no horizon (Wilson-Ewing, 2024). A plausible implication is that “Planck star remnant” currently names a family of closely related but not fully identical end-state proposals within effective loop-gravity models.

Several open issues recur across the literature. The detailed microphysics of the compact quantum transition region $R(t) = r_0 a(t).$2 remains under active development; existing spinfoam amplitudes are computed in truncations, and more refined numerics and topology-specific discretizations are still in progress (Rovelli et al., 2024). Extension to spinning and charged black holes is incomplete: Kerr and Reissner–Nordström geometries share similar inner/outer horizon structures, but a full Kerr quantum transition construction is pending (Rovelli et al., 2024). The precise external duration $R(t) = r_0 a(t).$3 still depends on the parameter $R(t) = r_0 a(t).$4 through $R(t) = r_0 a(t).$5, without a first-principles derivation of $R(t) = r_0 a(t).$6 from the quantum dynamics (Rovelli et al., 2024).

Cosmological viability also remains conditional. The 2024 review presents the PBH window $R(t) = r_0 a(t).$7–$R(t) = r_0 a(t).$8 as compatible with BBN, CMB, and structure formation at the level discussed there (Rovelli et al., 2024), and the Trivedi–Loeb paper argues qualitatively that PSR behave as cold dark matter and do not significantly affect $R(t) = r_0 a(t).$9 or microlensing observables (Trivedi et al., 3 Jun 2025). Yet the 2025 gravitational-wave analysis shows that the specific Gaussian PBH-formation route to PSR dark matter is excluded by LIGO O3, which implies that any successful PSR dark-matter scenario must invoke non-Gaussian primordial fluctuations or some other formation mechanism beyond the Gaussian narrow-peak picture (Trivedi et al., 24 Sep 2025).

Taken together, the current research presents PSR as a technically defined class of quantum-gravity remnants anchored in LQG/LQC structures—area quantization, critical-density bounce, and nonperturbative tunnelling—but not yet consolidated into a single universally accepted model. What is comparatively stable across the literature is the replacement of the singularity by Planckian quantum geometry, the emergence of a long-lived Planck-scale endpoint after Hawking evaporation, and the consequent possibility that such objects participate in the dark sector (Rovelli et al., 2024). What remains unsettled are the detailed endpoint geometry, the dominant cosmological production channel, the exact decay phenomenology, and the best observational strategy for testing the scenario.