On Saturday, July 18, 2020 at 6:18:28 AM UTC-6, Lawrence Crowell wrote:
>
> The tortoise coordinates is found from the Schwarzschild metric
>
> ds^2 = (1 - 2m/r)dt^2 - (1 - 2m/r)^{-1}dr^2 - r^2dΩ^2
>
> where for a signal leaving a point near the black hole with ds = 0 (null
> path) and propagating radially out, dΩ = 0, we have dt = dr/(1 - 2m/r)
> which then leads to
>
> T = t - t0 - 2m ln|r - 2m|.
>
> That is the tortoise coordinate. Please look this up to read further. I
> can't spend beaucoup time going over this for weeks to come.
>
> LC
>
You don't have to. We're done. But you should IMO address Brent's
objection, maybe on another thread. AG
> On Friday, July 17, 2020 at 11:08:00 PM UTC-5 [email protected] wrote:
>
>>
>>
>> On Friday, July 17, 2020 at 11:54:20 AM UTC-6, Lawrence Crowell wrote:
>>>
>>> On Friday, July 17, 2020 at 11:43:48 AM UTC-5 [email protected] wrote:
>>>
>>>>
>>>>
>>>> On Friday, July 17, 2020 at 5:34:17 AM UTC-6, Alan Grayson wrote:
>>>>>
>>>>>
>>>>>
>>>>> On Friday, July 17, 2020 at 4:48:51 AM UTC-6, Lawrence Crowell wrote:
>>>>>>
>>>>>> On Friday, July 17, 2020 at 5:01:41 AM UTC-5 [email protected]
>>>>>> wrote:
>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> On Thursday, July 16, 2020 at 7:50:07 PM UTC-6, Alan Grayson wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> On Thursday, July 16, 2020 at 5:08:57 PM UTC-6, Lawrence Crowell
>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>> Gravitons do not escape from a BH, any more than can light.
>>>>>>>>> However, from the perspective of an outside observer all matter than
>>>>>>>>> went
>>>>>>>>> into a BH is on the surface above the event horizon, called the
>>>>>>>>> stretched
>>>>>>>>> horizon.
>>>>>>>>>
>>>>>>>>> LC
>>>>>>>>>
>>>>>>>>
>>>>>>>> Gravitons might not exist (and hence quantum gravity can't exist)
>>>>>>>> But whatever the case, how can BH's interact gravitationally with
>>>>>>>> objects
>>>>>>>> beyond its event horizon? You say this doesn't happen. I don't
>>>>>>>> understand
>>>>>>>> your argument. AG
>>>>>>>>
>>>>>>>
>>>>>> That you are saying this illustrates you do not understand general
>>>>>> relativity.
>>>>>>
>>>>>>
>>>>>>>
>>>>>>> I may have identified the thousand pound gorilla in the room; the
>>>>>>> hypothetical force carrying particle of the quantum gravitating field,
>>>>>>> the
>>>>>>> graviton, which for BH's doesn't exert any force! AG
>>>>>>>
>>>>>>
>>>>>> I have no idea why you are saying this. Gravitation is not a force in
>>>>>> the usual sense and so the graviton does not produce a force in the
>>>>>> standard meaning. For the weak field limit the nonlinear terms are
>>>>>> negligable and a gravitational wave is linear. This is easily quantized.
>>>>>> In
>>>>>> fact it is similar to the Hanbury-Brown and Twiss theory of the
>>>>>> diphoton.
>>>>>> It is when the field becomes strong that general relativity becomes
>>>>>> nonlinear and runs into trouble with quantum mechanics.
>>>>>>
>>>>>> LC
>>>>>>
>>>>>
>>>>> I assumed a quantum field theory of gravity must have a particle
>>>>> associated with it, and that this particle is called the graviton.
>>>>> Gravity
>>>>> is a fictitious force. So what would the role of the graviton be, if not
>>>>> to
>>>>> produce some force? If you detect gravitational waves, don't they consist
>>>>> of gravitons if a quantum theory of gravity exists, analogous to photons
>>>>> in
>>>>> EM waves? AG
>>>>>
>>>>
>>>> Before you can present yourself as deeply knowledgeable of GR, you
>>>> should be able to give a coherent account how presumably *isolated*
>>>> bodies such as BH's, can gravitationally interact with what's exterior to
>>>> them. If gravitons can't do that in the context of a quantum theory of
>>>> gravity, what can? AG
>>>>
>>>
>>> It is the delay or tortoise coordinate basis for an external observer.
>>>
>>
>> This is a tough subject to wrap one's head around. Wiki has a decent
>> article on it. There's an objective gravitational effect of a BH beyond its
>> event horizon. Are you claiming that the effect is only supported by theory
>> by a particular choice of coordinate system for an external observer? AG
>>
>>>
>>> LC
>>>
>>
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