Table Of ContentSpringer Theses
Recognizing Outstanding Ph.D. Research
Sumanta Chakraborty
Classical and Quantum
Aspects of Gravity
in Relation to the
Emergent Paradigm
Springer Theses
Recognizing Outstanding Ph.D. Research
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Sumanta Chakraborty
Classical and Quantum
Aspects of Gravity
in Relation to the Emergent
Paradigm
Doctoral Thesis accepted by
Jawaharlal Nehru University, Pune, India
123
Author Supervisor
Dr. SumantaChakraborty Prof. ThanuPadmanabhan
Department ofTheoretical Physics Inter-University Centre for Astronomyand
Indian Association for the Cultivation of Astrophysics (IUCAA)
Science Pune
Jadavpur, Kolkata, West Bengal India
India
ISSN 2190-5053 ISSN 2190-5061 (electronic)
SpringerTheses
ISBN978-3-319-63732-7 ISBN978-3-319-63733-4 (eBook)
DOI 10.1007/978-3-319-63733-4
LibraryofCongressControlNumber:2017946667
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To my grandparents—Prakash, Jharna, Samir
and Binapani—for their love,
inspiration and knowledge.
To my parents—Subenoy and Archana—for
everything.
To my cousins—Sukriti and Poulomi—for
their love and support.
’
Supervisor s Foreword
CombiningtheprinciplesofGeneralRelativityandQuantumTheory—thetwokey
developments in theoretical physics in twentieth century—is a major challenge
which has attracted the attention of the community for more than half a century.
Thesedecadesofexplorationhaveessentiallyledtoaseriesofresoundingfailures,
very often after a period of initial hope and hype with regard to each of the
approaches.(Infact,atanygiventimeduringlast50yearsorso,therewasasetof
people who were ‘true believers’ in some particular approach they were pursuing,
with the hope that the solution was just around the corner!). The current situation
actuallyhasahistoricparallel.Atleasttwiceinthehistoryofphysics,verytalented
people have got themselves stuck in a “local minimum” of a completely wrong
idea.Thefirstwasinthecaseofthecalorifictheoryforheat;thesecondwasinthe
theory of aether with matter arising as vortices and excitations of the aether.
Ibelievethecurrentlypopularparadigmsofquantumgravitybelongtoyetanother
case of very smart physicists pursuing very wrong ideas.
So what could be a possible alternative route which can lift us above the “local
minimum”? A major paradigm shift isrequired, which I can best illustrate with an
analogy. We know that the elasticity (or fluid mechanics) can be described as a
self-consistentphysicaltheoryintermsofasetofdynamicalequations.Ifonetakes
these equations as fundamental and applies the principles of quantum theory to
them, one will certainly discover interesting new phenomena, like, for example,
phonons and their interactions. However, such an approach will not lead us to the
quantum structure of matter. Similarly, there is sufficient evidence to suggest that
the dynamical equationsdescribing gravity (in a large class ofmodels including—
but not limited to—Einstein’s theory) have the same conceptual status as the
equations of elasticity or fluid mechanics. Reinterpreting gravitational field equa-
tionsusingtheprinciplesofquantumtheoryisanalogoustoattemptsinwhichone
is applying the quantum principles to the equations of, say, elasticity. While some
interesting new results will emerge, we will not discover the quantum nature of
spacetime by such an approach.
Whatisrequiredistore-examinecloselythestructureofgravitationaldynamics
andtrytolearnwhatittellsusaboutthemicroscopicstructureofspacetime.Sucha
vii
viii Supervisor’sForeword
top-down approach (in length scales) is precisely what Boltzmann used, to figure
out that matter is made of discrete degrees offreedom, because it exhibits thermal
phenomenon. The fact that null surfaces in a spacetime appear to be hot to certain
observers holds the key to the understanding of the microstructure of spacetime.
Onlyaformalism which(i)recognizesthisfactupfront and(ii) canadopt itselfto
an observer dependent thermodynamics of spacetime will ever have a chance of
succeedingincombiningtheprinciplesofgravityandquantumtheory.Mostofthe
popularmodelsofquantumgravity,whichcameandwent(orontheirway-out!)in
the last five decades, did not do justice to this fact.
I and my collaborators have been exploring, since 2002, several aspects of this
alternative paradigm in which the thermodynamics of null surfaces plays a crucial
role. SumantaChakraborty’sthesis dealtwithseveralaspects ofthisparadigmina
nice and comprehensivemanner. Thefirstpart of thethesis providesthenecessary
broad introduction and the remaining chapters of the thesis deal directly with
several questions which are vital to the emergent paradigm of gravity.
In particular, Sumanta has made a significant amount of progress in extending
theemergentparadigmtoaclassofmodelscalledtheLanczos-Lovelockmodelsof
gravity. These are theories of gravity in which the field equations remain second
order in time but the entropy of the horizon is not proportional to its area. In the
literature,oneoftenfindsveryimaginativepiecesofresearchwhich—unfortunately—
are strongly linked to the idea that the entropy of a horizon is proportional to its
area.TheLanczos-Lovelockmodelsofgravitytakeyououtofthecomfort-zonein
whichentropyissuchanicegeometricalquantity,viz.thehorizonarea.Sotheyact
as a viable test-bed for the ideas of emergent gravity. If any of the ideas or the
resultswhichonecomeupwith,holdsonlyinEinstein’sGeneralRelativitybutnot
in the Lanczos-Lovelock models of gravity, I would treat it with caution. It is
therefore remarkable—and gratifying—that virtually every key idea within the
emergent paradigm developed by our group could be extended to
Lanczos-Lovelock models of gravity and Sumanta’s thesis contains several
examples of this extension. In a broader context, this fact tells you that the ther-
modynamic connection transcends Einstein’s theory and should be viewed as a
more fundamental feature of spacetime, not too closely linked to the specific field
equations describing the gravitational dynamics.
IenjoyedworkingwithSumantathroughhisPh.D.phaseandIwishhimallthe
bestinhisfuturecareer.IalsocongratulateSpringerforhavingthisprogramme,of
bringing out good theses as books, which both provides an encouragement to the
students as well as creating topical reference works for the community.
Prof. Thanu Padmanabhan
Thesis Advisor
Inter-University Centre for Astronomy
and Astrophysics (IUCAA), Pune, India
Preface
General Relativity (GR) is a very successful theory and is the best formalism we
have to describe the geometrical properties of the spacetime. It has passed all the
experimental and observational scrutinies so far, ranging from local tests like
perihelion precession and bending of light to precision tests using pulsars.
Inspiteoftheseoutstandingsuccessestherestillremainsomeunresolvedissues,
suggestingthatgeneralrelativityisnotcomplete.Themostimportantreasonisthe
presence of singularities in many physical situations leading to a loss of pre-
dictability. Another reason has to do with the fact that the horizons in general
relativity possess thermodynamic properties like temperature and entropy. Within
the framework of general relativity, there is no natural explanation for this “ther-
modynamic” interpretation and it provides motivation to take a fresh look at the
theory. A third reason arises from the fact that all the other known interactions
(electromagnetic, weak and strong) are described by quantum theories, while
gravityaloneisstilldescribedbyaclassicaltheory.Thislaidthefoundationofthe
belief that “quantum theory of gravity” awaits discovery. The attempts to obtain a
perturbative quantum general relativity, taking a cue from the quantization of the
other forces, has not succeeded. This has the unavoidable conclusion: we need to
modify our understanding of quantum field theory or the understanding of general
relativity or both.
In this thesis, we try to understand the thermodynamic nature of general rela-
tivity better by taking a closer look at the structure of general relativity and its
higher curvature cousins, collectively called Lanczos-Lovelock gravity. If one can
derive a result in the context of Lanczos-Lovelock gravity, the result for general
relativity is encompassed by it as well. We shall analyze the geometrical structure
ofLanczos-Lovelockgravity(whichhasgeneralrelativityasaspecialcase)leading
to the inescapable connection between gravity and thermodynamics. We will also
have occasion to talk about Virasoro algebra associated with an arbitrary null
surface and associated entropy in this context.
As a complementary approach towards a quantum theory of gravity, we study
some aspects of quantum field theory in curved spacetime. The specific issues
addressedinthis contextinclude: (a) What canwe sayaboutclassical singularities
ix
x Preface
from the viewpoint of quantum theory? This specifically requires one to probe
quantumfieldsinsidetheblackholehorizon.(b)Istheretrievalofinformationfrom
an evaporating black hole possible? (We will show that distortions to the thermal
spectra of a particular kind, referred to as non-vacuum distortions can be used to
fully reconstruct a subspace of initial data.) (c) Can Rindler effect be present for
geodesic observers? We illustrate for a specific (1+1) black hole spacetime, there
aregeodesicobserverswhoareconfinedtoaflatregionofthespacetimeandhence
will experience Rindler effect.
Finally,inorder tocapturesome quantumgravityeffects,we haveintroduced a
zeropointlengthtothespacetimeandhavediscusseditsgeometricalconsequences.
In particular, we have shown that at the Planck scale the spacetime becomes
essentially two-dimensional.
Kolkata, India Sumanta Chakraborty
