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IS THE VALIDITY OF THE FIRSTIS THE VALIDITY OF THE FIRST

LAW OF THERMODYNAMICSLAW OF THERMODYNAMICS

IMPLIES THE GENERALIZEDIMPLIES THE GENERALIZED

SECOND LAW OFSECOND LAW OF

THERMODYNAMICS OF THETHERMODYNAMICS OF THEUNIVERSE BOUNDED BY THEUNIVERSE BOUNDED BY THE

EVENT HORIZON?EVENT HORIZON?

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Introduction

Introduction:-

In this work we are dealing with the validity

of the generalized second law of thermodynamicson the Event horizonof the universe where we

have already assumed the validity of the first lawof thermodynamics on the Apparent horizon.

Here the Universe is taken as homogeneous andisotropic thermodynamical system filled with

perfect fluid.

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y Temperature (T)

(T=Hawking Temperature) (=Surface gravity)

y Entropy (S) A(S=Bekensteins Entropy) (A=Area)

y Relation (T,S,M) First Law of Thermodynamics

y Thermodynamic quantities ----- Geometry ofHorizon

(T and S) characterized

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The firstThe first law of thermodynamics Einstein Field Equationslaw of thermodynamics Einstein Field Equations

((QQ == TTddss))

-- Showed byShowed by T. JacobsonT. Jacobson in 1995in 1995 Phys. Rev.Phys. Rev. LettLett.. 75 126075 1260

Einstein Field Equations The first law of thermodynamicsEinstein Field Equations The first law of thermodynamics

on the horizonon the horizon

-- Showed byShowed by PadmanavanPadmanavan in 2002in 2002

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Assume Universe as a ThermodynamicalSystem

y At the apparent horizon RA:

y Hawking temperature TA= 1 2RA

y Entropy SA

= RA

2 G

y The first law of thermodynamics FriedmannEquations

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y Standard Big Bang Model :- Cosmological EventHorizon does not exists

y Accelerating Universe :- (i) Event horizon separatesfrom the Apparent horizon: RE > RA

(ii) First and Second law ofthermodynamics breaks down on the event horizon.

- Showed byWang B, Gong Yand Abdalla E 2006 Phys. Rev. D 74 083520

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y Universe bounded by Apparent horizon is a Bekenstein System :-

Bekensteins entropy or mass bound : S 2REentropy or area bound : S A 4

y

Temperature and Entropy should be modified at the eventhorizon to establish

Black hole Thermodynamics Space timeGeometry(on the event horizon)

y Generalized Second Law of Thermodynamics (GSLT) :-

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y FRW Line element :

area radius

hab = diag , k =0, + 1 and -1 corresponds

to the flat, closed andopen model

y Friedmann Equations :

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y Energy Conservation Equation :

y Apparent horizon :

y Event horizon :

y Hubble horizon :

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or

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y The amount of energy crossing the event horizon in time dt is

y First law of Thermodynamics :

So

y Gibbs equation :

wherever

So

- dE = 4 p rE3H r + p dt = - H - k

a2rE3H

Gdt

dQ = - dE = T EdS E

d S E = - H - ka 2

r E3

HG T E

d t

T E d S I = d E I + p d V

V=

4 p rE3

3 and EI =

4 p rE3 r

3

dSI = -rE

2

G TE H

-

k

a2 d r

E - H r

E dt

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y Total Entropy Variation :-

Where we have used the relation

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y For flat FRW Universe theGSLT is valid if the weakenergy condition is satisfied.

y For closed FRW model GSLT will be valid if

either (i) and weakenergy condition

is satisfied.

or (ii) and violation of weak energy

condition.

y No explicit expression of and is needed.

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Modified Friedmann equations in (n+1) dimensions are

Modified energy conservation equation is

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In this case the total entropy variation:

where is the volume ofann-dimensional

unitball.

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Thank YouThank you