Small Schwarzschild Research Articles

A metric for gravitational collapse around a Schwarzschild black hole

We consider the problem of gravitational collapse of a fluid under the effect of a small Schwarzschild black hole (e.g. a primordial one). We assume the fluid initially may be approximated by a uniform homogeneous dust. Starting from this configuration we obtain a class of metrics under some physically justified assumptions. We find that the metric we obtain includes the dust collapse as a subcase. After discussing some basic properties of the solution, we discuss the case of dust collapse in more detail. We find that the radial and tangential pressures outside the horizon may take positive or negative values depending on the values of the parameters.

Black holes in new massive conformal gravity

We investigate the black holes in the new massive conformal gravity which is not invariant under conformal transformations because of the presence of the Einstein-Hilbert term. First, we show that the small Schwarzschild black hole is unstable against the $s$-mode of linearized Ricci tensor by solving the Lichnerowicz-Ricci tensor equation. This instability induces the appearance of the non-BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole that has both Ricci tensor and conformal scalar hair.

A proposal of the gauge theory description of the small Schwarzschild black hole in AdS5 \xd7 S5

Based on 4d mathcal{N} = 4 SYM on {mathbb{R}}^1times {mathrm{S}}^3 , a gauge theory description of a small black hole in AdS5×S5 is proposed. The change of the number of dynamical degrees of freedom associated with the emission of the scalar fields’ eigenvalues plays a crucial role in this description. By analyzing the microcanonical ensemble, the Hagedorn behavior of long strings at low energy is obtained. Modulo an assumption based on the AdS/CFT duality for a large black hole, the energy of the small ten-dimensional Schwarzschild black hole E ∼ 1/(G10,NT7) is derived. A heuristic gauge theory argument supporting this assumption is also given. The same argument applied to the ABJM theory correctly reproduces the relation for the eleven-dimensional Schwarzschild black hole. One of the consequences of our proposal is that the small and large black holes are very similar when seen from the gauge theory point of view.

On the generalized wormhole in the Eddington-inspired Born–Infeld gravity

In this paper, we wish to investigate certain observable effects in the recently obtained wormhole solution of the Eddington-inspired Born–Infeld (EiBI) theory, which generalizes the zero-mass Ellis–Bronnikov wormhole of general relativity. The solutions of EiBI theory contain an extra parameter κ having the inverse dimension of the cosmological constant Λ, and which is expected to modify various general relativistic observables such as the masses of wormhole mouths, tidal forces and light deflection. A remarkable result is that a non-zero κ could prevent the tidal forces in the geodesic orthonormal frame from becoming arbitrarily large near a small throat radius () contrary to what happens near a small Schwarzschild horizon radius (). The role of κ in the flare-out and energy conditions is also analyzed, which reveals that the energy conditions are violated. We show that the exotic matter in the EiBI wormhole cannot be interpreted as a phantom () or ghost field ϕ of general relativity due to the fact that both ρ and pr are negative for all κ.

Lumpy AdS5× S5 black holes and black belts

Sufficiently small Schwarzschild black holes in global AdS5×S5 are Gregory-Laflamme unstable. We construct new families of black hole solutions that bifurcate from the onset of this instability and break the full SO(6) symmetry group of the S5 down to SO(5). These new “lumpy” solutions are labelled by the harmonics ℓ. We find evidence that the ℓ = 1 branch never dominates the microcanonical/canonical ensembles and connects through a topology-changing merger to a localised black hole solution with S8 topology. We argue that these S8 black holes should become the dominant phase in the microcanonical ensemble for small enough energies, and that the transition to Schwarzschild black holes is first order. Furthermore, we find two branches of solutions with ℓ = 2. We expect one of these branches to connect to a solution containing two localised black holes, while the other branch connects to a black hole solution with horizon topology S4 × S4 which we call a “black belt”.

SPACETIME NONCOMMUTATIVE EFFECT ON BLACK HOLE AS PARTICLE ACCELERATORS

We study the spacetime noncommutative effect on black hole as particle accelerators and, find that the particles falling from infinity with zero velocity cannot collide with unbound energy, either near the horizon or on the prograde ISCO when the noncommutative Kerr black hole is exactly extremal. Our results also show that the bigger of the spinning black hole's mass is the higher of center of mass energy that the particles obtain. For small and medium noncommutative Schwarzschild black hole, the collision energy depends on the black hole's mass.

Rotating black holes on codimension 2 branes

It has recently been demonstrated that certain types of nontensional stress-energy can live on tensional codimension-2 branes, including gravitational shockwaves and small Schwarzschild black holes. In this paper we generalize the earlier Schwarzschild results, and construct the exact gravitational fields of small rotating black holes on a codimension-2 brane. We focus on the phenomenologically interesting case of a three-brane embedded in a spacetime with two compactified extra dimensions. For a nonzero tension on the brane, we verify that these solutions also show the ``lightning rod'' effect found in the Schwarzschild solutions, the net effect of which is to rescale the fundamental Planck mass. This allows for larger black hole parameters, such as the event horizon, angular momentum, and lifetime than would be naively expected for a tensionless brane. It is also found that a black hole with angular momentum pointing purely along the brane directions has a smaller horizon angular velocity than the corresponding tensionless case, while a hole with bulk components of angular momentum has a larger angular velocity.

Black hole/string transition for the small Schwarzschild black hole of AdS 5 × S5 and critical unitary matrix models

In this paper we discuss the black hole–string transition of the small Schwarzschild black hole of AdS 5×S5 using the AdS/CFT correspondence at finite temperature. The finite temperature gauge theory effective action, at weak and strong coupling, can be expressed entirely in terms of constant Polyakov lines which are SU(N) matrices. In showing this we have taken into account that there are no Nambu–Goldstone modes associated with the fact that the 10-dimensional black hole solution sits at a point in S5. We show that the phase of the gauge theory in which the eigenvalue spectrum has a gap corresponds to supergravity saddle points in the bulk theory. We identify the third order N=∞ phase transition with the black hole–string transition. This singularity can be resolved using a double scaling limit in the transition region where the large N expansion is organized in terms of powers of N-2/3. The N=∞ transition now becomes a smooth crossover in terms of a renormalized string coupling constant, reflecting the physics of large but finite N. Multiply wound Polyakov lines condense in the crossover region. We also discuss the implications of our results for the resolution of the singularity of the lorenztian section of the small Schwarzschild black hole.

Gravitational magnetic monopoles and Majumdar-Papapetrou stars

During the 1990s a large amount of work was dedicated to studying general relativity coupled to non-Abelian Yang-Mills type theories. Several remarkable results were accomplished. In particular, it was shown that the magnetic monopole, a solution of the Yang-Mills-Higgs equations can indeed be coupled to gravitation. For a low Higgs mass it was found that there are regular monopole solutions, and that for a sufficiently massive monopole the system develops an extremal magnetic Reissner-Nordström quasihorizon with all the matter fields laying inside the horizon. These latter solutions, called quasi-black holes, although nonsingular, are arbitrarily close to having a horizon, and for an external observer it becomes increasingly difficult to distinguish these from a true black hole as a critical solution is approached. However, at precisely the critical value the quasi-black hole turns into a degenerate space-time. On the other hand, for a high Higgs mass, a sufficiently massive monopole develops also a quasi-black hole, but at a critical value it turns into an extremal true horizon, now with matter fields showing up outside. One can also put a small Schwarzschild black hole inside the magnetic monopole, the configuration being an example of a non-Abelian black hole. Surprisingly, Majumdar-Papapetrou systems, Abelian systems constructed from extremal dust (pressureless matter with equal charge and energy densities), also show a resembling behavior. Previously, we have reported that one can find Majumdar-Papapetrou solutions which are everywhere nonsingular, but can be arbitrarily close of being a black hole, displaying the same quasi-black-hole behavior found in the gravitational magnetic monopole solutions. With the aim of better understanding the similarities between gravitational magnetic monopoles and Majumdar-Papapetrou systems, here we study a particular system, namely a system composed of two extremal electrically charged spherical shells (or stars, generically) in the Einstein-Maxwell-Majumdar-Papapetrou theory. We first review the gravitational properties of the magnetic monopoles, and then compare with the gravitational properties of the double extremal electric shell system. These quasi-black-hole solutions can help in the understanding of true black holes, and can give some insight into the nature of the entropy of black holes in the form of entanglement.

Fermion absorption cross section of a Schwarzschild black hole

We study the absorption of massive spin-half particles by a small Schwarzschild black hole by numerically solving the single-particle Dirac equation in Painleve-Gullstrand coordinates. We calculate the absorption cross section for a range of gravitational couplings Mm/m_P^2 and incident particle energies E. At high couplings, where the Schwarzschild radius R_S is much greater than the wavelength lambda, we find that the cross section approaches the classical result for a point particle. At intermediate couplings we find oscillations around the classical limit whose precise form depends on the particle mass. These oscillations give quantum violations of the equivalence principle. At high energies the cross section converges on the geometric-optics value of 27 \pi R_S^2/4, and at low energies we find agreement with an approximation derived by Unruh. When the hole is much smaller than the particle wavelength we confirm that the minimum possible cross section approaches \pi R_S^2/2.

Quasinormal modes of a small Schwarzschild–anti-de Sitter black hole

We compute the quasinormal modes associated with the decay of the massless scalar field around a small Schwarzschild--anti-de Sitter black hole. The computations show that when the horizon radius is much less than the anti--de Sitter radius, the imaginary part of the frequency goes to zero as ${r}_{+}^{d\ensuremath{-}2}$ while the real part of $\ensuremath{\omega}$ decreases to its minimum and then goes to $d\ensuremath{-}1.$ Thus the quasinormal modes approach the usual AdS modes in the limit ${r}_{+}\ensuremath{\rightarrow}0.$ This agrees with suggestions of Horowitz and Hubeny [Phys. Rev. D 62, 024027 (2000)].

Object picture of quasinormal ringing on the background of small Schwarzschild anti–de Sitter black holes

We investigate the evolution of a scalar field propagating in small Schwarzschild anti--de Sitter black holes. The imaginary part of the quasinormal frequency decreases with the horizon size and the real part of the quasinormal frequency keeps nearly as a constant. The object picture clarifies the question about the quasinormal modes for small anti--de Sitter black holes. The dependence of the quasinormal modes on spacetime dimensions and the multipole index for small anti--de Sitter black holes is also illustrated.

Distortion in the Metric of a Small Center of Gravitational Attraction due to its Proximity to a Very Large Mass

The problem of two bodies in general relativity in an especially restricted mode is analyzed. One body is of small mass, and, under the influence of gravitational attraction, moves toward a much larger mass whose field produces ``tidal'' deformations in the geometry of the smaller one. To evaluate these deformations, we treat the Schwarzschild metric of the particle by a perturbation analysis similar to that performed by Regge and Wheeler. The boundary conditions for this analysis are obtained from the metric of the background field expressed in a novel set of comoving coordinates, here called Fermi normal coordinates. These coordinates have been described in the previous paper. In this paper we use the Schwarzchild metric given there in comoving coordinates as an asymptotic approximation for the full solution which is evaluated here. A perturbation analysis using the ``tidal deformation'' (background curvature) as an expansion parameter is performed on the metric of a small Schwarzschild particle. The solution so obtained satisfies Einstein's equations for empty space for small deviations from a nonflat metric. This solution also reduces to the Fermi metric in the appropriate limit, namely, when the ``distance'' from the geodesic is large compared to the radius of the small mass but small compared to the separation of the two masses. Thus only the quadratic terms in the distance are important. This solution is then used to find the deformations in shape of the throat of the wormhole and to locate this region of symmetry (the throat) by finding a coordinate transformation which leaves the metric invariant.