Theorem For Black Holes Research Articles

Notes on no black hole theorem in three dimensional gravity

In this paper, we revisit the no black hole theorem in three dimensional (3D) gravity in the Newman-Penrose formalism in a generalized Newman-Unti gauge. After adapting the well established 4D NP formalism and its gauge and coordinates system to 3D gravity, we show that the no black hole theorem is manifest in the NP equations. We further study in detail the horizon properties of the 3D charged rotating solutions and confirm that a black hole solution requires a negative cosmological constant.

A ‘black hole theorem,’ and its implications

A general formulation of the basic conflict of the information problem is given, encapsulated in a ‘black hole theorem.’ This is framed in a more general context than the usual one of quantum field theory on a background, and is based on describing a black hole as a quantum subsystem of a larger system, including its environment. This sharpens the limited set of possible consistent options; as with the Coleman-Mandula theorem, the most important point is probably the loophole in the ‘theorem,’ and what this tells us about the fundamental structure of quantum gravity. This ‘theorem’ in particular involves the general question of how to define quantum subsystems in quantum gravity. If black holes do behave as quantum subsystems, at least to a good approximation, evolve unitarily, and do not leave remnants, the ‘theorem’ implies the presence of interactions between a black hole and its environment that go beyond a description based on local quantum fields. This provides further motivation for and connects to previous work giving a principled parameterization of these interactions, and investigating their possible observational signatures via electromagnetic or gravitational wave observations of black holes.

Holographic bound on area of a compact binary merger remnant

Using concomitantly the generalized second law of black hole thermodynamics and the holographic Bekenstein entropy bound embellished by loop quantum gravity corrections to quantum black hole entropy, we show that the boundary cross sectional area of the postmerger remnant formed from the compact binary merger in gravitational wave detection experiments like GW150914 et seq., by the LIGO-VIRGO collaboration, is bounded from below. This lower bound is more general than the bound obtained from application of Hawking's classical area theorem for black holes, since it does not depend on whether the inspiralling compact binary pair or the postmerger remnant consists of black holes or other exotic compact objects. The derivation of the bound entails an estimate of the entropy of the gravitational waves emitted during the binary merger, which adapts to gravitational waves an extant formalism proposed originally for particle ensembles. The results for the minimal cross sectional area of the merger remnant due to binary compact mergers observed recently by the LIGO-VIRGO collaboration are discussed. While accurate measurement of the mass of the remnant for the binary neutron star merger GW170817 remains a challenge, we provide a proof of principle that for binary neutron star mergers our lower bound on the cross sectional area of the remnant provides an alternative approach to probe the validity of neutron star equations of state, independent of the tidal deformabilities of the components.

No inner-horizon theorem for black holes with charged scalar hairs

We establish a no inner-horizon theorem for black holes with charged scalar hairs. Considering a general gravitational theory with a charged scalar field, we prove that there exists no inner Cauchy horizon for both spherical and planar black holes with non-trivial scalar hair. The hairy black holes approach to a spacelike singularity at late interior time. This result is independent of the form of scalar potentials as well as the asymptotic boundary of spacetimes. We prove that the geometry near the singularity takes a universal Kasner form when the kinetic term of the scalar hair dominates, while novel behaviors different from the Kasner form are uncovered when the scalar potential become important to the background. For the hyperbolic horizon case, we show that hairy black hole can only has at most one inner horizon, and a concrete example with an inner horizon is presented. All these features are also valid for the Einstein gravity coupled with neutral scalars.

Analysis for Science Librarians of the 2020 Nobel Prize in Physics: Luminous Bodies, Black Holes, and How They Come Together at the Milky Way’s Heart

ABSTRACT The 2020 Nobel Prize in Physics was awarded to Roger Penrose, Reinhard Genzel, and Andrea Ghez. Penrose was awarded half of the Nobel Prize for creating a groundbreaking black hole theorem that drew on a half-century of theoretical speculations about singularities in general relativity. Ghez and Genzel share the remaining half of the prize for their research teams’ decades of precise observations of the center of the Milky Way, determining from stellar orbits that a supermassive compact object lies at the heart of the galaxy, consistent with predictions for a roughly 4 million solar-mass black hole. This paper describes the science behind the prize, each scientist’s career, and concludes with a citation analysis of each laureate that draws on Web of Science and Scopus data.

Limiting Case of the Spin Hypersurface Dirac Operator arising in the positive mass theorem for black holes

AbstractIn this paper, we give an explicit form of the scalar curvaure for the limiting case of the eigenvalue of the hypersurface Dirac operator which arises in the positive mass theorem for black holes. Then, we show that the hypersurface is an Einstein.

Aspects of multimode Kerr ringdown fitting

A black hole that is ringing down to quiescence emits gravitational radiation of a very specific nature that can inform us of its mass and angular momentum, test the no-hair theorem for black holes, and perhaps even give us additional information about its progenitor system. This paper provides a detailed description of, and investigation into the behavior of, multimode fitting of the ring-down signal provided by numerical simulations. We find that there are at least three well-motivated multimode fitting schemes that can be used. These methods are tested against a specific numerical simulation to allow for comparison to prior work.

Obstructions towards a generalization of no-hair theorems: Scalar clouds around Kerr black holes

We show that the integral method used to prove the no-hair theorem for black holes (BH's) in spherically symmetric and static spacetimes within the framework of general relativity with matter composed by a complex-valued scalar-field does not lead to a straightforward conclusion about the absence of hair in the stationary and rotating (axisymmetric) scenario. We argue that such a failure can be used to justify in a simple and heuristic way the existence of nontrivial boson clouds or hair found numerically by Herdeiro and Radu [Phys. Rev. Lett. 112, 221101 (2014); Classical Quantum Gravity 32, 144001 (2015)] and analytically by Hod in the test field limit [Phys. Rev. D 86, 104026 (2012); Phys. Rev. D 86, 129902(E) (2012); Eur. Phys. J. C 73, 2378 (2013); J. High Energy Phys. 01 (2017) 030]. This is due to the presence of a contribution that is negative when rotation exists which allows for an integral to vanish even when a nontrivial boson hair is present. The presence of such a negative contribution that depends on the rotation properties of the BH is perfectly correlated with the eigenvalue problem associated with the boson-field equation. Conversely, when the rotation is absent the integral turns to be composed only by non negative (i.e., positive semidefinite) terms and thus the only way it can vanish is when the hair is completely absent. This analysis poses serious challenges and obstructions towards the elaboration of no-hair theorems for more general spacetimes endowed with a BH region even when including matter fields that obey the energy conditions. Thus rotating boson stars, if collapsed, may lead indeed to a new type of rotating BH, like the ones found in [Phys. Rev. Lett. 112, 221101 (2014); Classical Quantum Gravity 32, 144001 (2015)]. In order to achieve this analysis we solve numerically the eigenvalue problem for the boson field in the Kerr-BH background by imposing rigorous regularity conditions at the BH horizon for the non-extremal case ($0<a<M$) which include the near extremal one in the limit $M\ensuremath{\rightarrow}a$, as well as the small BH limit $M\ensuremath{\rightarrow}a\ensuremath{\rightarrow}0$.

A new singularity theorem for black holes which allows chronology violation in the interior

The interior of the Kerr solution is singular and achronological. The classic singularity theorem by Hawking and Penrose relies on chronology, and thus does not apply to the Kerr solution. An improvement of their theorem by Kriele partially removes the requirement of chronology. However, both of these singularity theorems fail to give any information on the type or location of the incomplete geodesics. Here, using recent results of Minguzzi, we prove a new singularity theorem, specifically designed to apply to black holes, which enables locating null incomplete geodesics within the black hole interior, all the while allowing certain forms of chronology violation in the interior.

Geometrothermodynamics for black holes and de Sitter space

A general method to extract thermodynamic quantities from solutions of the Einstein equation is developed. In 1994, Wald established that the entropy of a black hole could be identified as a Noether charge associated with a Killing vector of a global space-time (pseudo-Riemann) manifold. We reconstruct Wald’s method using geometrical language, e.g., via differential forms defined on the local space-time (Minkowski) manifold. Concurrently, the abstract thermodynamics are also reconstructed using geometrical terminology, which is parallel to general relativity. The correspondence between the thermodynamics and general relativity can be seen clearly by comparing the two expressions. This comparison requires a modification of Wald’s method. The new method is applied to Schwarzschild, Kerr, and Kerr–Newman black holes and de Sitter space. The results are consistent with previous results obtained using various independent methods. This strongly supports the validity of the area theorem for black holes.

A no-hair theorem for black holes in f(R) gravity

In this work we present a no-hair theorem which discards the existence of four-dimensional asymptotically flat, static and spherically symmetric or stationary axisymmetric, non-trivial black holes in the frame of gravity under metric formalism. Here we show that our no-hair theorem also can discard asymptotic de Sitter stationary and axisymmetric non-trivial black holes. The novelty is that this no-hair theorem is built without resorting to known mapping between gravity and scalar–tensor theory. Thus, an advantage will be that our no-hair theorem applies as well to metric models that cannot be mapped to scalar–tensor theory.

No hair theorems for a static and stationary reflecting star

We prove the non existence of massive scalar, vector and tensor hairs outside the surface of a static and stationary compact reflecting star. Our result is the extension of the no hair theorem for black holes to horizonless compact configurations with reflecting boundary condition at the surface. We also generalize the proof for spacetimes with a positive cosmological constant.

No-hair theorem for black holes in astrophysical environments.

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

A no black hole theorem

We show that one cannot put a stationary (extended) black hole inside certain gravitating flux-tubes. This includes an electric flux-tube in five-dimensional Einstein–Maxwell theory, as well as the standard flux-branes of string theory. The flux always causes the black hole to grow indefinitely. One finds a similar restriction in a Kaluza–Klein setting where the higher dimensional spacetime contains no matter.

Bekenstein–Hawking entropy in expanding universes from black hole theorems

We show that the use of suitable theorems for black hole formation in Friedmann expanding universes leads to a modification of the Bekenstein–Hawking entropy. By adopting an argument similar to the original Bekenstein one, we write down the expression for the Bekenstein–Hawking entropy suitable for non-static isotropic expanding universes together with the equation of state of a black hole. This equation can be put in a form similar to the one of an ideal gas but with a factor depending on the Hubble radius. Moreover, we give some argument on a possible relation between our entropy expression and the Cardy–Verlinde one. Finally, we explore the possibility that primordial inflation is due to black hole evaporation in our context.

You Cannot Press Out the Black Hole

It is shown that a ball-shaped black hole region homeomorphic with D**n cannot be pressed out, along whichever axis penetrating the black hole region, into a black ring with a doughnut-shaped black hole region homeomorphic with S**1 x D**(n-1). A more general prohibition law for the change of the topology of black holes, including a version of no-bifurcation theorems for black holes, is given.

No-hair theorems for black holes in the Abelian Higgs model

Motivated by the study of holographic superconductors, we generalize no-hair theorems for minimally coupled scalar fields charged under an Abelian gauge field, in arbitrary dimensions and with arbitrary horizon topology. We first present a straightforward generalization of no-hair theorems for neutral scalar hair. We then consider the existence of extremal black holes with scalar hair, and in the case of horizons with zero or positive curvature, provide a bound on the mass and charge of the scalar field that are necessary for the scalar hair to develop.

Electric charge in interaction with magnetically charged black holes

We examine the angular momentum of an electric charge e placed at rest outside a dilaton black hole with magnetic charge Q. The electromagnetic angular momentum which is stored in the electromagnetic field outside the black hole shows several common features regardless of the dilaton coupling strength, though the dilaton black holes are drastically different in their spacetime structure depending on it. First, the electromagnetic angular momentum depends on the separation distance between the two objects and changes monotonically from eQ to 0 as the charge goes down from infinity to the horizon, if rotational effects of the black hole are discarded. Next, as the black hole approaches extremality, however, the electromagnetic angular momentum tends to be independent of the distance between the two objects. It is then precisely $eQ$ as in the electric charge and monopole system in flat spacetime. We discuss why these effects are exhibited and argue that the above features are to hold in widely generic settings including black hole solutions in theories with more complicated field contents, by addressing the no hair theorem for black holes and the phenomenon of field expulsion exhibited by extremal black holes.

Towards a novel no-hair theorem for black holes

We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.

HORIZON MASS THEOREM

A new theorem for black holes is found. It is called the horizon mass theorem. The horizon mass is the mass which cannot escape from the horizon of a black hole. For all black holes, neutral, charged or rotating, the horizon mass is always twice the irreducible mass observed at infinity. Previous theorems on black holes are: (i) the singularity theorem, (ii) the area theorem, (iii) the uniqueness theorem, (iv) the positive energy theorem. The horizon mass theorem is possibly the last general theorem for classical black holes. It is crucial for understanding Hawking radiation and for investigating processes occurring near the horizon.