Gravitational Diffraction Radiation

in Higher-Dimensions

Jun-Qi Guo

The University of MississippiV. Cardoso, M. Cavaglià, J-Q. Guo, to be submitted.

The 16th Midwest Relativity Meeting, Washington University in St. Louis

Outline

Introduction Computation of the field Computation of the Poynting vector Discussion Summary

Introduction

Image particle

particle

Smooth hidden brane

particle

Higher dimensional spacetime

Computation of the field

( )( ) ( ( ))DpS x g d x x

( )D S x ( ) ( , ) ( )DD p D p px d x G x x S x

( ) ?D x :DG Green Function

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D=even

D=odd

Difference between and D evenSpacetime

D oddSpacetime

4

1( )

4G t R

R

3 2 2

1( )

2G t R

t R

Computation of the field

2 2( )

2 22 / 2

2

1 1 1 1( ) ( ) ( )

2 2

D D

D D DG z O

RR

4( )2 2

22 / 2

2

1 ( ) 1( ) ( ) [ ] ( )

2 2

DD

D D D

g zx d O

RR

For D=even

0 0 ( )p pz x x x x where

pR x x

Computation of the field

2 4

2 22 / 2

2

1 1 1 1 1( ) ( ) ( ) ( )

2 2

D D

D D D

g dx O

B d B RR

(1 )B n v where

Recurrence relation

A general formula for ( )D x

:Lorentz factor

2 / 2

1 1 1( ) ( ) ( )

2D D D

dx O

BR d R

Computation of the field

Computation of the Poynting vector

D DT

D x D

n

B

/ 2

1( )x D D

OR

22D DR n

22DD

dBR

d

22D DD

d dR

dt dt

?T

2

2

D

D emit

dP Bn T R

d

222 22

1 1 1( ) [( ) ]

4 2

DDg d

BB d B

2 2 22

1(2 ) ( )D D

T n R OR

222 22

2 1

1 1 1 1 1( ) [( ) ] ( )

4 2

DD

D D

g dn O

R B d B R

Computation of the Poynting vector

D=4,

Discussion

2 2 2

2 2 52

[ ( (1 ) )]

16 (1 )

dP g a n v v n

d n v

D=6,

2 2

4 8 74

[ 3 ]

64 (1 )

dP g CF EH

d n v

2 44 ( ) ( )( )

( )(1 )

n a n a a vC a v

n v

(1 )F n v

2 2[ (1 ) ]E a v n v n a

(1 )

EH

n v

0a 0

D even

dP

d

Discussion

emit

dPP d

d

2 24 24 2

12 12D

emit

g gP r a

D=4,

D=6,

For circular motion with constant

speed:

r

Extra

dimension

space?

26 6 2 2 2

2(1 4 )

120D

emit

gP r r

22 2

2(1 4 )

120

gv a

Summary(I)

Find general formulae for and in higher dimensional flat spacetime.

Check that when , .

Find two interesting physical differences between and ;

between and .

D even D evenT

0D evenT

0a

4D

emitP

6D even

emitP

evenSpacetime

oddSpacetime

Odd dimensions

Curved spacetime

Application: gravitational wave background

Summary(II)--next