Emergence of the fuzzy horizon through gravitational collapse

In this article we present a self contained review of the principles of Matrix Theory including the basics of light cone quantization, the formulation of 11 dimensional M-Theory in terms of supersymmetric quantum mechanics, the origin of membranes and the rules of compactification on 1,2 and 3 tori. We emphasize the unusual origins of space time and gravitation which are very different than in conventional approaches to quantum gravity. Finally we discuss application of Matri...

D0-brane gas picture of Schwarzschild black hole (SBH) is considered in the large N regime of Matrix theory. An entropy formula, which reproduces the thermodynamics of SBH in the large N limit for all dimensions ($D\geq 6$), is proposed. The equations of states for low temperature are obtained. We also give a proof of the Newton gravitation law between two SBHs, whose masses are not equal. Our result in some extent supports that the physics of Matrix theory is Lorentz invaria...

In this article we study correspondence between the microscopic spectrum and macroscopic properties of a class of extremal and non-extremal black branes and outline an origin of the interactions among various microstates of a given black brane configuration from the perspective of an intrinsic Riemannian geometry arising from the coarse graining entropy over a large number of microstates. We have analyzed the state-space geometry in the case of various extremal and non-extrem...

We consider membranes of spherical topology in uncompactified Matrix theory. In general for large membranes Matrix theory reproduces the classical membrane dynamics up to 1/N corrections; for certain simple membrane configurations, the equations of motion agree exactly at finite N. We derive a general formula for the one-loop Matrix potential between two finite-sized objects at large separations. Applied to a graviton interacting with a round spherical membrane, we show that ...

We propose a large $N$ quantum mechanics of non-abelian bosonic and fermionic variables as a model for quantum gravity. The theory admits fuzzy sphere as static solution. Over the fuzzy geometry, the quantum mechanics of the fermions is given by a sum of oscillators with equal frequency. The energy state where exactly half of the Fermi sea is filled contains the maximal amount of degeneracy. This state of the fuzzy sphere obeys the mass-radius relation of a Schwarzschild blac...

This thesis addresses some classical and semi-classical aspects of black holes using an effective membrane representation of the event horizon. The classical "membrane paradigm" equations are derived from an underlying action formulation, even though the equations are dissipative. It is shown how the membrane action can also account for the hole's entropy, including the numerical factor. Two short derivations of Hawking radiation are then presented, the first based on particl...

Computations in general relativity have revealed an interesting phase diagram for the black hole - black string phase transition, with three different black objects present for a range of mass values. We can add charges to this system by `boosting' plus dualities; this makes only kinematic changes in the gravity computation but has the virtue of bringing the system into the near-extremal domain where a microscopic model can be conjectured. When the compactification radius is ...

It has been suggested in the literature that, given a black hole spacetime, a relativistic membrane can provide an effective description of the horizon dynamics. In this paper, we explore such a framework in the context of a 2+1-dimensional BTZ black hole. Following this membrane prescription, we are able to translate the horizon dynamics (now described by a string) into the convenient form of a 1+1-dimensional Klein-Gordon equation. We proceed to quantize the solutions and c...

Combining a variety of results in string theory and general relativity, a picture of the black hole interior is developed wherein spacetime caps off at an inner horizon, and the inter-horizon region is occupied by a Hagedorn gas of a very low tension state of fractionated branes. This picture leads to natural resolutions of a variety of puzzles concerning quantum black holes. Gravity Research Foundation 2015 Fourth Prize Award for Essays on Gravitation.

We consider the physics of a matrix model describing D0-brane dynamics in the presence of an RR flux background. Non-commuting spaces arise as generic soltions to this matrix model, among which fuzzy spheres have been studied extensively as static solutions at finite N. The existence of topologicaly distinct static configurations suggests the possibility of D-brane topology change within this model, however a dynamical solution interpolating between topologies is still somewh...