arXiv subjects

S. Kalyana Rama

Publications and source records attributed to S. Kalyana Rama.

At least 19 recordsLinked to original sources

arXiv2020

Non singular, bouncing M theory universe

We propose a set of equations as a simple model for non singular evolutions of a $10 + 1$ dimensional M theory universe. Our model uses ideas from Loop Quantum Cosmology and offers a solution to the important problem of singularity resolutions. We solve the equations numerically and find that an M theory universe in this model evolves non singularly and with a bounce : going back in time, its density reaches a maximum and decreases thereafter whereas its physical size reaches a non vanishing minimum and increases thereafter. Taking the constituents of the universe to be the most entropic ones (which are four sets of intersecting M branes) leads to an effectively $3 + 1$ dimensional spacetime as the M theory universe expands, both in the infinite past and future.

hep-th↗

arXiv2019

Black hole or Fuzz ball or a Loop quantum star ? Assessing the fate of a massive collapsing star

Using the effective equations in our Loop Quantum Cosmology (LQC) -- inspired models, we resolve the $(n + 2)$ dimensional black hole singularity. This resolution in the four dimensional case is same as that given recently by Ashtekar, Olmedo, and Singh. We then study the fate of a massive collapsing star in $(n + 2)$ dimensions, focussing on a singularity resolved black hole, a string theoretic fuzz ball, and a Loop quantum star -- which is a solution to the the effective modified equations for static spherically symmetric stars we obtained recently using LQC ideas. We find qualitatively that a massive collapsing star is likely to become a Loop quantum star : it is likely to have a macroscopic core region with Planckian densities and pressures which is surrounded by a low density corona region extending to the Schwarzschild radius.

gr-qc↗

arXiv2019

LQ Stars : Modifying the Tolman -- Oppenheimer -- Volkoff equations a la LQC

We rewrite the Tolman -- Oppenheimer -- Volkoff (TOV) equations for four and higher dimensional static spherically symmetric stars so that they resemble the equations for anisotropic cosmology. This becomes possible by treating the curvature terms of the sphere as part of the matter sector. Comparing then with the effective equations in the Loop Quantum Cosmology -- inspired models, we propose analogous modifications to the TOV equations which contain one arbitrary function. A linear function gives the TOV equations. If the function and all its derivatives are finite then the solutions are non singular. For $sin \; x \;$, an `image star' appears beyond the central region of maximal pressures in the original star. This is evocative of a bouncing universe in Loop Quantum Cosmology. We discuss possible observational consequences of these features.

gr-qc↗

arXiv2019

Non singular M theory Universe in Loop Quantum Cosmology -- inspired Models

We study an M theory universe in the Loop Quantum Cosmology -- inspired models which involve a function, the choice of which leads to a variety of evolutions. The M theory universe is dominated by four stacks of intersecting brane--antibranes and, in general relativity, it becomes effectively four dimensional in future while its seven dimensional internal space reaches a constant size. We analyse the conditions required for non singular evolutions and obtain explicit solutions in the simplified case of a bi--anisotropic universe and a piece--wise linear function for which the evolutions are non singular. One may now ask whether the physics in the Planckian regime can enhance the internal volume to phenomenologically interesting values. In the simplified case considered here, there is no non trivial enhancement. We make some comments on it.

hep-th↗

arXiv2018

Isotropic LQC and LQC--inspired Models with a massless scalar field as Generalised Brans--Dicke theories

We explore whether generalised Brans -- Dicke theories, which have a scalar field $Φ$ and a function $ω(Φ)$, can be the effective actions leading to the effective equations of motion of the LQC and the LQC--inspired models, which have a massless scalar field $σ$ and a function $f(m) \;$. We find that this is possible for isotropic cosmology. We relate the pairs $(σ, f)$ and $(Φ, ω)$ and, using examples, illustrate these relations. We find that near the bounce of the LQC evolutions for which $f(m) = sin \; m$, the corresponding field $Φ\to 0$ and the function $ω(Φ) \propto Φ^2 \;$. We also find that the class of generalised Brans -- Dicke theories, which we had found earlier to lead to non singular isotropic evolutions, may be written as an LQC--inspired model. The relations found here in the isotropic cases do not apply to the anisotropic cases, which perhaps require more general effective actions.

gr-qc↗

arXiv2017

Variety of $(d + 1)$ dimensional Cosmological Evolutions with and without bounce in a class of LQC -- inspired Models

The bouncing evolution of an universe in Loop Quantum Cosmolgy can be described very well by a set of effective equations, involving a function $sin \; x$. Recently, we have generalised these effective equations to $(d + 1)$ dimensions and to any function $f(x) \;$. Depending on $f(x) \;$ in these models inspired by Loop Quantum Cosmolgy, a variety of cosmological evolutions are possible, singular as well as non singular. In this paper, we study them in detail. Among other things, we find that the scale factor $a(t) \; \propto \; t^{ \frac {2 q} {(2 q - 1) \; (1 + w) d}} \;$ for $f(x) = x^q \;$, and find explicit Kasner--type solutions if $w = 2 q - 1 \;$ also. A result which we find particularly fascinating is that, for $f(x) = \sqrt{x} \;$, the evolution is non singular and the scale factor $a(t)$ grows exponentially at a rate set, not by a constant density, but by a quantum parameter related to the area quantum.

gr-qc↗

arXiv2016

A Class of LQC--inspired Models for Homogeneous, Anisotropic Cosmology in Higher Dimensional Early Universe

The dynamics of a (3 + 1) dimensional homogeneous anisotropic universe is modified by Loop Quantum Cosmology and, consequently, it has generically a big bounce in the past instead of a big-bang singularity. This modified dynamics can be well described by effective equations of motion. We generalise these effective equations of motion empirically to (d + 1) dimensions. The generalised equations involve two functions and may be considered as a class of LQC -- inspired models for (d + 1) dimensional early universe cosmology. As a special case, one can now obtain a universe which has neither a big bang singularity nor a big bounce but approaches asymptotically a `Hagedorn like' phase in the past where its density and volume remain constant. In a few special cases, we also obtain explicit solutions.

gr-qc↗

arXiv2015

On the Stability of (M theory) Stars against Collapse : Role of Anisotropic Pressures

Unitarity of evolution in gravitational collapses implies existence of macroscopic stable horizonless objects. With such objects in mind, we study the effects of anisotropy of pressures on the stability of stars. We consider stars in four or higher dimensions and also stars in M theory made up of (intersecting) branes. Taking the stars to be static, spherically symmetric and the equations of state to be linear, we study `singular solutions' and the asymptotic perturbations around them. Oscillatory perturbations are likely to imply instability. We find that non oscillatory perturbations, which may imply stability, are possible if an appropriate amount of anisotropy is present. This result suggests that it may be possible to have stable horizonless objects in four or any higher dimensions, and that anisotropic pressures may play a crucial role in ensuring their stability.

hep-th↗

arXiv2015

Singularity Resolution + Unitary Evolution + Horizon = Firewall ?

We assume that a quantum gravity theory exists where evolutions are unitary, no information is lost, singularities are resolved, and horizons form. Thus a massive star will collapse to a black hole having a horizon and an interior singularity--resolved region. Based on unitarity and on a postulated relation, we obtain an evolution equation for the size of this region. As the black hole evolves by evaporation and accretions, this region grows, meets the horizon, and becomes accessible to an outside observer. The required time is typically of the order of black hole evaporation time. If the boundary of the singularity--resolved region can be considered as the firewall of Almheiri et al then this marks the appearance of a firewall.

hep-th↗

arXiv2014

Massive Compact Objects in a Quantum Theory of Gravity

A massive compact object is that which forms when a sufficiently massive star collapses. This is commonly taken to be a black hole with a singularity surrounded by a horizon and which evolves by emitting Hawking radiation. In a quantum theory of gravity, singularities are expected to be resolved and the evolutions are expected to be unitary. Assuming that such a theory with these properties exists, and with a few more physically motivated assumptions, we argue that a massive compact object has no singularity (by assumption) and must also have no horizon; otherwise, there may be a loss of predictability in the case of a black hole candidate observed today. With no singularity and also with no horizon, the massive compact object will then evolve as a standard quantum system with large number of interacting degrees of freedom.

gr-qc↗

arXiv2014

A simple derivation of the strong subadditivity inequalities

In this short note, we give a simple derivation of the strong subadditivity inequalities: S(13) + S(23) \ge S(1) + S(2) and S(12) + S(23) \ge S(2) + S(123). The simplicity is due to the way we represent the quantum systems. We make a few remarks about such a representation.

quant-ph↗

arXiv2014

Stars in M theory (made up of intersecting branes)

We study stars in M theory. First, we obtain the analog of Oppenheimer -- Volkoff equations in a suitably general set up. We obtain analytically the asymptotic solutions to these equations when the equations of state are linear. We study perturbations around such solutions in several examples and, following a standard method, use their behaviour to determine whether an instability is present or not. In this way, we obtain a generalisation of the corresponding results of Chavanis. We also find that stars in M theory have instabilities. Therefore, if sufficiently massive, such stars will collapse. We discuss the significance of these (in)stabilities within the context of Mathur's fuzz ball proposal.

hep-th↗

arXiv2014

Remarks on Black Hole Evolution a la Firewalls and Fuzzballs

Assume that there exists a fundamental theory of gravity which has a fundamental length scale and which is capable of explaining black hole evolution process fully in terms of fundamental microscopic degrees of freedom. The resultant evolution will clearly be unitary and will have no information loss. Carrying this assumption to its logical conclusion and, in particular, by considering the size of the region obtained by resolving the black hole singularity in such a theory, we arrive at a scenario very similar to that in Mathur's fuzz ball proposal where there is no horizon. We also comment on the consistency of such a picture with the recent results of Almheiri et al.

hep-th↗

arXiv2013

M theory Branes : U duality properties and a class of new Static Solutions

We obtain the most general static intersecting brane solutions by directly solving the relevant equations of motion analytically and in complete generality. These solutions reduce to the known ones in special cases, and contain further a class of new static solutions which are horizonless. We describe their properties and discuss their physical relevance. Along the way, we also describe the features of the brane energy momentum tensors, the equations of motion, and their solutions which arise as consequences of the intersection rules and the U duality symmetries of M theory.

hep-th↗

arXiv2012

General Static (Intersecting) Brane Solutions

We present one extra parameter worth of new static brane and intersecting brane solutions in string/M theory. These general solutions may be obtained by solving the equations of motion directly. But, in this letter, we first obtain the general eleven dimensional vacuum solutions, and then generate the brane solutions by U duality operations -- namely boosting, dimensional reduction and uplifting, and S and T dualties. Such general solutions will be needed in the study of higher dimensional brane stars and their collapse.

hep-th↗

arXiv2012

Static brane--like vacuum solutions in D \ge 5 dimensional spacetime with positive ADM mass but no horizon

We describe static, brane--like, solutions to vacuum Einstein's equations in D = n + m + 2 dimensional spacetime with m \ge 2 and n \ge 1. These solutions have positive ADM mass but no horizon. The curvature invariants are finite everywhere except at r = 0 where r is the radial coordinate in the m + 1 dimensional space. The presence of n \ge 1 extra dimensions is crucial for these properties. Such solutions may be naturally anticipated if Mathur's fuzzball proposal for black holes is correct.

hep-th↗

arXiv2011

Strong Coupling BCS Superconductivity and Holography

We attempt to give a holographic description of the microscopic theory of a BCS superconductor. Exploiting the analogy with chiral symmetry breaking in QCD we use the Sakai-Sugimoto model of two D8 branes in a D4 brane background with finite baryon number. In this case there is a new tachyonic instability which is plausibly the bulk analog of the Cooper pairing instability. We analyze the Yang-Mills approximation to the non-Abelian Born-Infeld action. We give some exact solutions of the non-linear Yang-Mills equations in flat space and also give a stability analysis, showing that the instability disappears in the presence of an electric field. The holograhic picture also suggests a dependence of $T_c$ on the number density which is different from the usual (weak coupling) BCS. The flat space solutions are then generalized to curved space numerically and also, in an approximate way, analytically. This configuration should then correspond to the ground state of the boundary superconducting (superfluid) ground state. We also give some preliminary results on Green functions computations in the Sakai - Sugimoto model without any chemical potential

hep-th↗

arXiv2010

10 + 1 to 3 + 1 in an Early Universe with mutually BPS Intersecting Branes

We assume that the early universe is homogeneous, anisotropic, and is dominated by the mutually BPS 22'55' intersecting branes of M theory. The spatial directions are all taken to be toroidal. Using analytical and numerical methods, we study the evolution of such an universe. We find that, asymptotically, three spatial directions expand to infinity and the remaining spatial directions reach stabilised values. Any stabilised values can be obtained by a fine tuning of initial brane densities. We give a physical description of the stabilisation mechanism. Also, from the perspective of four dimensional spacetime, the effective four dimensional Newton's constant G_4 is now time varying. Its time dependence will follow from explicit solutions. We find in the present case that, asymptotically, G_4 exhibits characteristic log periodic oscillations.

hep-th↗