Evasion of No-Hair Theorems and Novel Black-Hole Solutions in Gauss-Bonnet Theories (1711.03390v2)

Abstract: We consider a general Einstein-scalar-GB theory with a coupling function f(\phi). We demonstrate that black-hole solutions appear as a generic feature of this theory since a regular horizon and an asymptotically-flat solution may be easily constructed under mild assumptions for f(\phi). We show that the existing no-hair theorems are easily evaded, and a large number of regular, black-hole solutions with scalar hair are then presented for a plethora of coupling functions f(\phi).

• The paper demonstrates how scalar-Gauss-Bonnet couplings allow regular black-hole solutions with non-trivial scalar hair, evading classical no-hair theorems.
• It employs analytical methods and numerical integration to validate solutions exhibiting regular horizons and asymptotic flatness.
• The findings imply observable deviations from General Relativity, opening new avenues for gravitational wave and astronomical tests.

Evasion of No-Hair Theorems and Novel Black-Hole Solutions in Gauss-Bonnet Theories

The paper "Evasion of No-Hair Theorems and Novel Black-Hole Solutions in Gauss-Bonnet Theories" by Antoniou, Bakopoulos, and Kanti explores a significant development in the domain of black-hole physics within modified theories of gravity. In this work, the authors address the longstanding notion of no-hair theorems, which suggest that black holes, devoid of electromagnetic fields, should be simple and possess only three observable parameters: mass, charge, and angular momentum. This paper focuses on extensions of General Relativity, specifically Gauss-Bonnet (GB) theories which include couplings with scalar fields, to demonstrate how these theorems can be evaded.

Key Contributions and Findings

1. Einstein-scalar-Gauss-Bonnet Model: The authors explore a modified gravity theory where traditional Einstein gravity is supplemented with a scalar field coupled to a quadratic GB term. This coupling is guided by an arbitrary function $f(\phi)$, allowing a broad class of scalar-Gauss-Bonnet theories to be considered.
2. Evasion of No-Hair Theorems: The paper demonstrates that regular black-hole solutions, characterized by a non-trivial scalar field or 'scalar hair', can be consistently constructed within these theories. These solutions effectively bypass traditional no-hair arguments due to the properties of the scalar-Gauss-Bonnet interaction, which alters the dynamics both near the black-hole horizon and at infinity.
3. Asymptotic Behavior: The paper details the construction of these black-hole solutions, illustrating that a regular event horizon and asymptotic flatness are achievable for a diverse set of coupling functions $f(\phi)$. In particular, the constraints necessary for avoiding no-hair theorems are clearly defined, which are instrumental in finding viable solutions.
4. Numerical Demonstrations: The authors perform numerical integrations to validate their theoretical arguments, producing black-hole solutions with different functional forms for $f(\phi)$. This not only emphasizes the theoretical robustness of their approach but also provides a practical example of how specific scalar-Gauss-Bonnet theories manifest in terms of black-hole solutions.

Implications and Future Directions

The findings of this paper suggest notable implications for our understanding of black holes in alternative theories of gravity. The ability to evade no-hair theorems implies that black holes could indeed possess additional 'hair', potentially detectable by future gravitational wave observatories or other astronomical tools. Such discoveries could offer new insights into the nature of gravity and fundamental physics.

Additionally, the bounded nature of black-hole masses predicted by this theory suggests observable deviations from General Relativity at small scales, offering a fertile ground for future observational studies. Testing these theories with empirical data could provide constraints on the parameters of such theories or even uncover novel gravitational phenomena.

Looking forward, the expansion of these findings into scenarios incorporating charged black holes or rotating solutions could further enrich this field of paper. Moreover, the integration of these solutions into cosmological models or their implications in the high-energy regime could present exciting challenges and opportunities for further research.

In summary, this paper contributes significantly to theoretical explorations of black holes in modified gravity theories, paving the way for more inclusive models that expand upon the conventional understanding limited by no-hair theorems.