BMS-like structures in cosmology Batrice Bonga ICERM Workshop - - PowerPoint PPT Presentation

▶
bms like structures in cosmology
SMART_READER_LITE
LIVE PREVIEW

BMS-like structures in cosmology Batrice Bonga ICERM Workshop - - PowerPoint PPT Presentation

May 31, 2023 448 likes •808 views

BMS-like structures in cosmology Batrice Bonga ICERM Workshop Advances and Challenges in Computational Relativity September 15 2020 [BB+Prabhu, arXiv:2009.01243] Overview Asymptotic symmetries in cotmological spacetimes but

slide-1
SLIDE 1

BMS-like structures in cosmology

Béatrice Bonga ICERM Workshop “Advances and Challenges in Computational Relativity” – September 15 2020 [BB+Prabhu, arXiv:2009.01243]

slide-2
SLIDE 2

Asymptotic symmetries in cotmological spacetimes

Overview

but first some words about asymptotically flat spacetimes...

slide-3
SLIDE 3

From messy physics to peaceful real

slide-4
SLIDE 4

Key idea: bring infinity to a finite distance

slide-5
SLIDE 5

Asymptotic flatness

slide-6
SLIDE 6

Consequences

slide-7
SLIDE 7

This is common to all asymptotically flat spacetimes

Universal structure

Gravitational radiation is encoded in the next-order structure and differs from spacetime to spacetime

slide-8
SLIDE 8

Others examples: Kerr-Newman spacetimes, Weyl spacetimes, etc.

Example: flat spacetime

slide-9
SLIDE 9

Generic asymptotically flat spacetime

slide-10
SLIDE 10

Generic asymptotically flat spacetime

slide-11
SLIDE 11

Two definitions are equivalent!

Vestibulum congue Vestibulum congue Vestibulum congue Vestibulum congue

Coordinate description à la Bondi & Sachs Geometric description à la Penrose (with the conformal completion)

slide-12
SLIDE 12

“Spacetime diffeomorphism that leave the universal structure at scri invariant”

Asymptotic symmetry algebra

slide-13
SLIDE 13
  • Bigger than Poincare (=translations & rotations)
  • BMS = supertranslations & rotations

Bondi-Metzner-Sachs algebra (BMS)

supertranslations rotations

slide-14
SLIDE 14

It provides quantities with a physical interpretation!

What is BMS good for?

slide-15
SLIDE 15

Critical assumption

Move far away from sources: ‘spacetime becomes flat’

slide-16
SLIDE 16

Expanding spacetimes are not asymptotically flat!

slide-17
SLIDE 17

Why assume asymptotic flatness?

Conference Warsaw 1963

slide-18
SLIDE 18

Today: NO cosmological constant

slide-19
SLIDE 19

Decelerating FLRW spacetimes

slide-20
SLIDE 20
slide-21
SLIDE 21
slide-22
SLIDE 22
slide-23
SLIDE 23

The conformal factor

slide-24
SLIDE 24

Simple resolution

slide-25
SLIDE 25

For asymptotically flat spacetimes, should have a limit to but FLRW spacetimes are homogeneous, so there is matter everywhere!

Presence of matter

slide-26
SLIDE 26

Spacetimes with a cosmological null asymptote

cosmological

slide-27
SLIDE 27

Spacetimes with a cosmological null asymptote

cosmological

slide-28
SLIDE 28

Asymptotic symmetry algebra

slide-29
SLIDE 29

Didn’t we know this already?

slide-30
SLIDE 30

There is a twist!

slide-31
SLIDE 31

Not exactly BMS in cosmology

notion of mass and linear momentum?

slide-32
SLIDE 32

Class of spacetimes at least as big as asymptotically flat spacetimes!

Any other examples?

Linearization stability still open question

slide-33
SLIDE 33

❖ Geometric construction to study spacetimes beyond asymptotic flatness in the cosmological context ❖ Asymptotic symmetry algebra is BMS-like ➢ It does not have a translation subalgebra!

Conclusion

slide-34
SLIDE 34

Future applications

❖ Next order structure ➢ Study rigorously gravitational radiation produced by compact sources in cosmological spacetimes ➢ Study the gravitational memory effect ➢ Charges and fluxes ❖ Link with timelike future infinity ❖ … your favorite topic!