On what basis did you conclude that Girivraja is the same place as Rājagṛha?

@Bingming , In the Vālmīki Rāmāyaṇam 2.68.21 , The messangers of Ayodhyā are said to have reached "Girivraja" , although this Verse is not present in the Critical Addition. In the Critical the word "Girivraja" , as I've stated in the question occurs only once and that to for a city different from the Kekaya capital. Even in the Vulgate version of the Rāmāyaṇa , the name Girivraja occurs twice , once in 2.68.21 and other in the Bāla Kāṇḍa where it is used for a different city than the Kekaya metropolis.

Vālmīki Rāmāyaṇa doesn't mention Rājagṛha as the capital afaik, plus you equated both places, what was the basis of doing so? This question is still not answered.

@Bingming , well Rājagṛha is mentioned as the City where Bharata , Śatrughna , Bharata's uncle Yudhājit and Aśvapati Kaikeya were present. So it might be the capital. So is Girivraja a different city than Rājagṛha?

may I ask, what is the śloka where they are mentioned to be in Rājagṛha?

Anyway, I checked the commentaries on 2.68.21, the comms. Amṛtakataka and Tilaka state that Girivraja is Kekayapura and is also known as Rājagṛha. Other comms. such as Bhūṣaṇa, Tattvadīpikā, Śiromaṇī, etc. state that Girivraja is Kekayapura, but don't mention Rājagṛha.

@Bingming , in 2.70.1-2 , the messangers are said to have met Yudhājit in Rājagṛha.

Ny question still remains. As you said Both Rājagṛha and Girivraja are said to be Kekayapura. So is it a coincidence that in the Mahābhāratam , the capital of Magadha was mentioned as Girivraja and in later times ( or before, my knowledge is limited ) was known as Rājagṛha or is there a connection?

I think, it may be the same place, which is Rājagṛha in Mahābhārata too, but it has been a lot of time, many yugas, so the scenery might have changed a bit.

I meant, many yugas from Rāmāyaṇa

the problem would be that how can the two kingdoms Kekaya and Magadha have the same capital city?

or perhaps, the kingdom of Magadha had a different capital, during the time of Rāmāyaṇa

Can you elaborate on this? Like I don't really understand , Kekaya and Magadha have are very distinct location wise

hmm, the problem is that the Girivraja is said to be the capital of Magadha as well

in Mahābhārata, etc.

now, either there are two places with the name Girivraja, or Magadha's capital wasn't Girivraja, during the time of Rāmāyaṇa.

Does all this raise a question on Kaikeyī being a kekayan princess?

firstly, where is Kekaya exactly located? It's in north-western Bhārata right?

Kaikeyī was a princess of Kekaya, there is no doubt regarding that

Yes it was in the region of what is now the Jhelum district of Pakistan.

Still , the Rājagṛha and Magadha issue stays..

Rājagṛha and Girivraja issue*

it would be strange for a kingdom that northwest, to have a capital in the far-east, most likely Kekayapura (Girivraja) is not what's called Girivraja in Mahābhārata.

there being two locations of the same name

in other words, there's a Girivraja (Rājagṛha) in northwest India, and another in Magadha, that's east India

this wouldn't be really weird, after all there is a difference of more than 4 mahāyugas b/w Rāma and say Jarāsandha (who had his capital in Girivraja).

Could be , there's a research paper by H.D Sankalia

There this issue is discussed. There the scholar refered to "Toponymic transference" that occured between the names of the Kekaya and Magadha capitals.

Do the other versions of the Rāmāyaṇa have anything to say about Kaikeyī's home-kingdom , her father and also his brothers Yudhājit?