arXiv subjects

M. B. Paranjape

Publications and source records attributed to M. B. Paranjape.

At least 19 recordsLinked to original sources

arXiv2026

Zero Temperature, Degenerate Fermion Stars

We study a degenerate, zero temperature, fermion gas with rest mass $m$, that only interacts with itself, gravitationally. We describe a self-consistent novel approach to the formation of a degenerate, quantum mechanical, star. In this approach, the fermions occupy the energy levels that are determined by the self consistent gravitational interactions, according to the Pauli exclusion principle. Then in this novel approach, the size of the highest occupied level determines the radius of the star. In the Newtonian gravitational limit, the fermions feel a potential corresponding to a simple harmonic well that smoothly attaches in the exterior to the usual $1/r$ Newtonian gravitational potential. We find analytically, solutions for stars with any radius and mass, parametrized by $m$ and $N_s$, the total number of fermions. In the Newtonian limit, we easily find that we can construct a star that is more compact than the Buchdahl bound and indeed can even be smaller than the Schwarzschild radius. Clearly, such cases are outside of the purview of the Newtonian limit. Therefore we expand our analysis to fermions in the general relativistic context, interacting gravitationally with a metric. We consider the metric corresponding to the interior Schwarzschild solution smoothly connecting to the usual exterior Schwarzschild metric. Treating matter semi-classically, we recover the Buchdahl bound in a completely independent analysis. We briefly discuss classical stability of the Newtonian solution, and its relation to Newtonian polytropic fluids.

gr-qc↗

arXiv2026

Physics on manifolds with exotic differential structures

A given topological manifold can sometimes be endowed with inequivalent differential structures. Physically this means that what is meant by a differentiable function (smooth) is simply different for observers using inequivalent differential structures. {The 7-sphere, $\bS^7$, was the first topological manifold where the possibility of inequivalent differential structures was discovered \cite{Milnor}.} In this paper, we examine the import of inequivalent differential structures on the physics of fields obeying the Dirac equation on $\bS^7$. { $\bS^7$ is a fibre bundle of the 3-sphere as a fibre on the 4-sphere as a base. We consider the Kaluza-Klein limit of such a fibre bundle which reduces to a SO(4) Yang-Mills gauge theory over $\bS^4$. We find, for certain specific symmetric set of gauge potentials, that the spectrum of the Dirac operator can be computed explicitly, for each choice of the differential structure. Hence identical topological manifolds have different physical laws. We find this the most important conclusion of our analysis.

hep-th↗

arXiv2026

Reflecting Gravitons: The Graviton Laser and the Gertsenshtein effect

Graviton lasers have been considered in the past, \cite{gl}, but practical terrestrial implementations appear infeasible. The absence of any known mechanism to reflect gravitons means that it remains unclear how a graviton beam could be directed repeatedly through a putative lasing medium. Astrophysical graviton lasing is still a possibilty as circular graviton orbits around blackholes afford the possibility of an arbitrarily long path length through the lasing medium of ultra-light dark matter \cite{bhgl,nhaxs}. In this essay, we consider the possibility of a graviton laser that could be constructed in a laboratory setting. The graviton lasing medium could be one of many possible gravitating systems, of which we give three possible examples. We calculate the possibility of reflecting the gravitons by using the conversion of gravitons into photons in an external magnetic field, the Gertsenshtein effect, \cite{Gertsenshtein1962}. We may convert the gravitons to photons, then reflect the photons, then reconvert the photons into gravitons via the same effect, and then pass them through the graviton lasing medium. With an identical apparatus on the other side, we can essentially extend the path length of the gravitons through the lasing medium as arbitrarily long as desired.

gr-qc↗

arXiv2025

Graviton Scattering on Gravitational Atoms: Relic Graviton Shot Noise

We study the scattering of a graviton on a gravitational atom. By gravitational atom we mean a quantum mechanical system of a gravitational (bound) state of two massive particles, with possibly some boundary conditions (such as bouncing on a table or hanging as a pendulum). We demonstrate the unexpected fact, that the total absorption cross section is universal, it is independent of both the mass of the gravitationally bound particle or of the mass providing the binding potential. We find that the total absorption cross-section is simply proportional to the Planck area, multiplied by a dimensionless, numerical factor. We speculate about the potential for detection of relic gravitons shot noise.

hep-th↗

arXiv2024

Quintessence and the Higgs Portal in the Carroll limit

A cosmological model based on two scalar fields is proposed. The first of these, $φ$, has mass $μ$, while the second, $χ$, is massless. The pair are coupled through a ``Higgs portal''. First, we show how the model reproduces the Friedmann equations if the square of the mass of the $φ$ field is proportional to the cosmological constant and $χ$ represents the quintessence field. Quantum corrections break the conformal symmetry, and the $χ$ field acquires a mass equal to $\sqrt{3gΛ}$. The perturbative approach with $g\ll 1$ is consistent with the bounds for $m_χ$; moreover, by using dimensional analysis, we estimate $m_χ\ll H_0\approx 10^{-33}$ eV, which is in accordance with what is expected in the quintessence scenario. The acceleration of the universe is proportional to $χ^2$, we conclude that for very long times, the solution of the equation of motion approaches $\langle χ\rangle \sim {m_χ}/{\sqrtλ}$ and the universe continues to accelerate, with a constant acceleration.

hep-th↗

arXiv2024

Thin-Wall Monopoles in a False Vacuum

We study numerically the existence in a false vacuum, of magnetic monopoles which are ``thin-walled'', \ie, which correspond to a spherical region of radius $R$ that is essentially trivial surrounded by a wall of thickness $Δ\ll R$, hence the name thin wall, and finally an exterior region that essentially corresponds to a pure Abelian magnetic monopole. Such monopoles were dubbed false monopoles and can occur in non-abelian gauge theories where the symmetry-broken vacuum is actually the false vacuum. This idea was first proposed in \cite{Kumar:2010mv}, however, {the proof of the existence of thin-wall, false monopoles given there }was incorrect. Here we fill this lacuna and demonstrate numerically{, for an appropriately modifed potential,} the existence of thin-wall false monopoles. The decay via quantum tunnelling of the false monopoles could be of importance to cosmological scenarios which entertain epochs in which the universe is trapped in a symmetry broken false vacuum.

hep-th↗

arXiv2022

Near Zone Dynamical Effects in Gravity

Dynamical effects in general relativity have been finally, relatively recently observed by LIGO\cite{2016LRR....19....1A}. To be able to measure these signals, great care has to be taken to minimize all sources of noise in the detector. One of the sources of noise is called Newtonian noise. In this article we present an analysis of the dynamical (time dependent) nature of the Newtonian noise. In that respect, it is a misnomer to call it Newtonian noise, the Newtonian theory does not afford any dynamical notion of the gravitational field. The dynamical aspects of the nature of the Newtonian noise have heretofore been disregarded as they were considered negligible. However, we demonstrate that they are indeed not far from the realm of being measurable. They could be used to validate Einsteinian general relativity or to give valuable information on the true dynamical nature of gravity. One fundamental question, for example, is a direct measurement the speed of propagation of gravitational effects and the verification that it is indeed the same as the speed of light. We propose a simple laboratory experiment that could affirm or deny this proposition. We also analyze the possibility of the detection of large geophysical events, such as earthquakes. We find that large seismic events seem to be easily observable with the present ensemble of gravitational wave detectors,. The ensemble of gravitational wave detectors could easily serve as a system of early warning for otherwise catastrophic seismic events.

hep-th↗

arXiv2021

What is the Gravitational Field of a Mass in a Spatially Nonlocal Quantum Superposition?

The study of the gravitational field produced by a spatially non-local, superposed quantum state of a massive particle is a thrilling area of modern physics. One question to be answered is whether the gravitational field behaves as the classical superposition of two particles separated by a spatial distance with half the mass located at each position or as a quantum superposition with a far more interesting and subtle behaviour for the gravitational field. Quantum field theory is ideally suited to probe exactly this kind of question. We study the scattering of a massless scalar on such a spatially nonlocal, quantum superposition of a massive particle. We compute the differential scattering cross section corresponding to the interaction coming from the exchange of one graviton. We find that the scattering cross section is not at all represented by the Schrödinger-Newton picture of potential scattering from two localized sources with half the mass at each source. We discuss how our result would be lethal to the Schrödinger-Newton description of gravitation interacting with quantum matter and would be conducive to considering the gravitational field to be quantized. We comment on the experimental feasibility of observing such effects.

gr-qc↗

arXiv2021

Ferromagnetic instability in PAAI in the sky

We study an idealised plasma of fermions, coupled through an abelian gauge force $U(1)_X$, and which is asymmetric in that the masses of the oppositely charged species are greatly unequal. The system is dubbed PAAI, plasma asymétrique, abélien et idéalisé. It is argued that due to the ferromagnetic instability that arises, the ground state gives rise to a complex of domain walls. This complex being held together by stresses much stronger than cosmic gravity, does not evolve with the scale factor and along with the heavier oppositely charged partners simulates the required features of Dark Energy with mass scale for the lighter fermions in the micro-eV to nano-eV range. Further, residual $X$-magnetic fields through mixture with standard magnetic fields, can provide the seed for cosmic-scale magnetic fields. Thus the scenario can explain several cosmological puzzles including Dark Energy.

hep-th↗

arXiv2020

PAAI in the sky : towards a particulate mechanism for Dark Energy and concordant Dark Matter

We propose the origins of Dark Energy in a hidden sector with a pair of very light fermions, oppositely charged under an abelian gauge force $U(1)_X$ but of unequal mass. The system is dubbed PAAI, plasma which is abelian, asymmetric and idealised. For a range of the hidden fine structure constant values and the value of mass of the lightest fermion the PAAI is argued to simulate Dark Energy. Additional fermions from the same sector are shown to account for Dark Matter. Further, residual $X$-magnetic fields can mix with Maxwell electromagnetism to provides the seed for cosmic-scale magnetic fields. Thus the scenario can explain several cosmological puzzles from within the same hidden sector.

hep-ph↗

arXiv2020

You can see a clock running backwards in time

The epitome of acausal or anti-chronological behaviour would be to see a clock running backwards in time. In this essay we point out that this is indeed possible, but there is no problem with causality. What you see isn't what is really happening. Locally, causality is always respected. However our observation should be cause for pause to astronomers and cosmologists, who strictly observe events occurring at very large distances or very long ago and certainly not locally. It can be that what you see isn't what you necessarily get.

gr-qc↗

arXiv2020

Stable, thin wall, negative mass bubbles in de Sitter space-time

Negative mass makes perfect physical sense as long as the dominant energy condition is satisfied by the corresponding energy-momentum tensor. Heretofore, only {\it configurations} of negative mass had been found \cite{Belletete:2013nqa,Mbarek:2014ppa}, the analysis did not address stability or dynamics. In this paper, we analyze both of these criteria. We demonstrate the existence of {\it stable}, static, negative mass bubbles in an asymptotically de Sitter space-time. The bubbles are solutions of the Einstein equations and correspond to an interior region of space-time containing a specific mass distribution, separated by a thin wall from the exact, negative mass Schwarzschild-de Sitter space-time in the exterior. We apply the Israel junction conditions at the wall. For the case of an interior corresponding simply to de Sitter space-time with a different cosmological constant from the outside space-time, separated by a thin wall with energy density that is independent of the radius, we find static but unstable solutions which satisfy the dominant energy condition everywhere. The bubbles can collapse through spherically symmetric configurations to the exact, singular, negative mass Schwarzschild-de Sitter solution. Interestingly, this provides a counter-example of the cosmic censorship hypothesis. Alternatively, the junction conditions can be used to give rise to an interior mass distribution that depends on the potential for the radius of the wall. We show that for no choice of the potential, for positive energy density on the wall that is independent of the radius, can we get a solution that is non-singular at the origin. However, if we allow the energy density on the wall to depend on the radius of the bubble, we can find {\it stable}, static, non-singular solutions of negative mass which everywhere satisfy the dominant energy condition.

gr-qc↗

arXiv2019

Monopole operators and their symmetries in QED3-Gross-Neveu models

Monopole operators are topological disorder operators in 2+1 dimensional compact gauge field theories appearing notably in quantum magnets with fractionalized excitations. For example, their proliferation in a spin-1/2 kagome Heisenberg antiferromagnet triggers a quantum phase transition from a Dirac spin liquid phase to an antiferromagnet. The quantum critical point (QCP) for this transition is described by a conformal field theory: Compact quantum electrodynamics (QED3) with a fermionic self-interaction, a type of QED3-Gross-Neveu model. We obtain the scaling dimensions of monopole operators at the QCP using a state-operator correspondence and a large-N expansion, where 2N is the number of fermion flavors. We characterize the hierarchy of monopole operators at this SU(2) x SU(N) symmetric QCP.

cond-mat.str-el↗

arXiv2019

Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory

We study the quantum phase transition from a Dirac spin liquid to an antiferromagnet driven by condensing monopoles with spin quantum numbers. We describe the transition in field theory by tuning a fermion interaction to condense a spin-Hall mass, which in turn allows the appropriate monopole operators to proliferate and confine the fermions. We compute various critical exponents at the quantum critical point (QCP), including the scaling dimensions of monopole operators by using the state-operator correspondence of conformal field theory. We find that the degeneracy of monopoles in QED3 is lifted and yields a non-trivial monopole hierarchy at the QCP. In particular, the lowest monopole dimension is found to be smaller than that of QED3 using a large $N_f$ expansion where $2N_f$ is the number of fermion flavors. For the minimal magnetic charge, this dimension is $0.39N_f$ at leading order. We also study the QCP between Dirac and chiral spin liquids, which allows us to test a conjectured duality to a bosonic CP$^1$ theory. Finally, we discuss the implications of our results for quantum magnets on the Kagome lattice.

cond-mat.str-el↗

arXiv2019

Cosmic Ferromagnetism of Magninos

We study the physical conditions for the occurrence of ferromagnetic instability in a neutral plasma of fermions. We consider a system of two species $M$ and $Y$ which are oppositely charged under a local $U(1)_{X}$, with $M$ much lighter than $Y$. The leading correction to free quasiparticle behaviour for the lighter species arises from the exchange interaction, while the heavier species remain spectators. This plasma, which is abelian, asymmetric and idealised, is shown to be naturally susceptible to the formation of a completely spin-imbalanced ferromagnetic state for the lighter species (dubbed a magnino) in large parts of parameter space. It is shown that the domain structure formed by this ferromagnetic state can mimic Dark Energy, determining the masses of the two fermion species involved, depending on their abundance relative to the standard photons. Incomplete cancellation of the X-magnetic fields among the domains can give rise to residual long range $X$-magnetic fields. Under the assumption that this $U(1)_{X}$ mixes with Maxwell electromagnetism, this provides a mechanism for the seed for cosmic-scale magnetic fields. An extended model with several flavours $M_a$ and $Y_a$ of the species can incorporate Dark Matter. Thus the scenario shows the potential for explaining the large scale magnetic fields, and what are arguably the two most important outstanding puzzles of cosmology: Dark Matter and Dark Energy.

astro-ph.CO↗

arXiv2019

Vacuum Decay Induced by False Skyrmions

We consider the Skyrme model modified by the addition of mass terms which explicitly break chiral symmetry and pick out a specific point on the model's target space as the unique true vacuum. However, they also allow the possibility of false vacua, local minima of the potential energy. These false vacuum configurations admit metastable skyrmions, which we call false skyrmions. False skyrmions can decay due to quantum tunnelling, consequently causing the decay of the false vacuum. We compute the rate of decay of the false vacuum due to the existence of false skyrmions.

hep-th↗

arXiv2018

New sources of gravitational wave signals: The black hole graviton laser

A graviton laser works, in principle, by the stimulated emission of coherent gravitons from a lasing medium. For significant amplification, we must have a very long path length and/or very high densities. Black holes and the existence of weakly interacting sub-eV dark matter particles (WISPs) solve both of these obstacles. Orbiting trajectories for massless particles around black holes are well understood \cite{mtw} and allow for arbitrarily long graviton path lengths. Superradiance from Kerr black holes of WISPs can provide the sufficiently high density \cite{ABH}. This suggests that black holes can act as efficient graviton lasers. Thus directed graviton laser beams have been emitted since the beginning of the universe and give rise to new sources of gravitational wave signals. To be in the path of particularly harmfully amplified graviton death rays will not be pleasant.

gr-qc↗

arXiv2018

The twin paradox: the role of acceleration

The twin paradox, which evokes from the the idea that two twins may age differently because of their relative motion, has been studied and explained ever since it was first described in 1906, the year after special relativity was invented. The question can be asked: "Is there anything more to say?" It seems evident that acceleration has a role to play, however this role has largely been brushed aside since it is not required in calculating, in a preferred reference frame, the relative age difference of the twins. Indeed, if one tries to calculate the age difference from the point of the view of the twin that undergoes the acceleration, then the role of the acceleration is crucial and cannot be dismissed. In the resolution of the twin paradox, the role of the acceleration has been denigrated to the extent that it has been treated as a red-herring. This is a mistake and shows a clear misunderstanding of the twin paradox.

gr-qc↗